Theorem exp3acom23g 1371

Description: Implication form of exp3acom23 1372. (Contributed by Alan Sare, 22-Jul-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Assertion

Ref	Expression
exp3acom23g	⊢ ((φ → ((ψ ∧ χ) → θ)) ↔ (φ → (χ → (ψ → θ))))

Proof of Theorem exp3acom23g

Step	Hyp	Ref	Expression
1		ancomsimp 1369	. . 3 ⊢ (((ψ ∧ χ) → θ) ↔ ((χ ∧ ψ) → θ))
2		impexp 433	. . 3 ⊢ (((χ ∧ ψ) → θ) ↔ (χ → (ψ → θ)))
3	1, 2	bitri 240	. 2 ⊢ (((ψ ∧ χ) → θ) ↔ (χ → (ψ → θ)))
4	3	imbi2i 303	1 ⊢ ((φ → ((ψ ∧ χ) → θ)) ↔ (φ → (χ → (ψ → θ))))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by: (None)