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Metamath Proof Explorer

Theorem bianfd

Description: A wff conjoined with falsehood is false. (Contributed by NM, 27-Mar-1995) (Proof shortened by Wolf Lammen, 5-Nov-2013)

		Ref	Expression
	Hypothesis	bianfd.1	$⊢ φ \to \neg ψ$
	Assertion	bianfd	$⊢ φ \to (ψ \leftrightarrow (ψ \land χ))$

Step	Hyp	Ref	Expression
1		bianfd.1	$⊢ φ \to \neg ψ$
2	1	intnanrd	$⊢ φ \to \neg (ψ \land χ)$
3	1 2	2falsed	$⊢ φ \to (ψ \leftrightarrow (ψ \land χ))$