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Metamath Proof Explorer

Theorem simplbi2com

Description: A deduction eliminating a conjunct, similar to simplbi2 . (Contributed by Alan Sare, 22-Jul-2012) (Proof shortened by Wolf Lammen, 10-Nov-2012)

		Ref	Expression
	Hypothesis	simplbi2com.1	$⊢ φ \leftrightarrow (ψ \land χ)$
	Assertion	simplbi2com	$⊢ χ \to (ψ \to φ)$

Proof

Step	Hyp	Ref	Expression
1		simplbi2com.1	$⊢ φ \leftrightarrow (ψ \land χ)$
2	1	simplbi2	$⊢ ψ \to (χ \to φ)$
3	2	com12	$⊢ χ \to (ψ \to φ)$