Theorem simplbi2comg 1373

Description: Implication form of simplbi2com 1374. (Contributed by Alan Sare, 22-Jul-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Assertion

Ref	Expression
simplbi2comg	⊢ ((φ ↔ (ψ ∧ χ)) → (χ → (ψ → φ)))

Proof of Theorem simplbi2comg

Step	Hyp	Ref	Expression
1		bi2 189	. 2 ⊢ ((φ ↔ (ψ ∧ χ)) → ((ψ ∧ χ) → φ))
2	1	exp3acom23 1372	1 ⊢ ((φ ↔ (ψ ∧ χ)) → (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: (None)