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Metamath Proof Explorer

Theorem iffalsed

Description: Value of the conditional operator when its first argument is false. (Contributed by Glauco Siliprandi, 11-Dec-2019)

		Ref	Expression
	Hypothesis	iffalsed.1	$⊢ φ \to \neg χ$
	Assertion	iffalsed	$⊢ φ \to if (χ, A, B) = B$

Step	Hyp	Ref	Expression
1		iffalsed.1	$⊢ φ \to \neg χ$
2		iffalse	$⊢ \neg χ \to if (χ, A, B) = B$
3	1 2	syl	$⊢ φ \to if (χ, A, B) = B$