Theorem simplbi2com 1374

Description: A deduction eliminating a conjunct, similar to simplbi2 608. (Contributed by Alan Sare, 22-Jul-2012.) (Proof shortened by Wolf Lammen, 10-Nov-2012.)

Hypothesis

Ref	Expression
simplbi2com.1	⊢ (φ ↔ (ψ ∧ χ))

Assertion

Ref	Expression
simplbi2com	⊢ (χ → (ψ → φ))

Proof of Theorem simplbi2com

Step	Hyp	Ref	Expression
1		simplbi2com.1	. . 3 ⊢ (φ ↔ (ψ ∧ χ))
2	1	simplbi2 608	. 2 ⊢ (ψ → (χ → φ))
3	2	com12 27	1 ⊢ (χ → (ψ → φ))

Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  mo2  2233  2elresin  5195