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True/Flase: if a,b,c ⊨ d so at least one of this term is tautology: a→d or b→d or c→d

Maybe someone know how to proof that?

Thanks for help and have a good day!

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    What do you mean by "d is supposed to be false"? Who supposes that and why? – 2017-02-12
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    In my opinion this argument is False. so given a,b,c ⊨ d, and a,b,c can be contradiction and when 'd' can be False/Ture doesn't matter. if a,b,c is false so 'd' have to be False also in that case. – 2017-02-12
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    @KfirWilfand You seem to be contradicting yourself. First you say that it doesn't matter what $d$ is, then you say it is false, (both conclusions under the same assumption). What is it then? – 2017-02-12
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    If $0\to d$ is true, then you can't conclude whether $d$ is false or true, that's correct. – 2017-02-12
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    if you have False→d ,d can be false or true doesn't matter right? since everthing thing can cames from conclusions. so a,b,c if False 'd' can be whatever you like. and if I want one of this term to be tautology it's can happend only if 'd' is False – 2017-02-12
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    Actually i'm a little bit stuck. What do you think is the answer? – 2017-02-12
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    $a,b,c,d$ are propositional formulae or propositional variables ? In the second case, the result is straightforward: $a \to d$ can be a tautology only if $a=d$. – 2017-02-12
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    Thanks for your help! Unfortunately a,b,c,d are propositional formulae – 2017-02-12

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If $a,b,c,d$ are formulae, we can show that it does not hold, manufacturing a simple counterexample.

Consider as $d$ the formula: $a \land b \land c$; clearly:

$a,b,c \vDash a \land b \land c$

but $a \nvDash a \land b \land c$, and the same for $b$ and $c$.