Theorem exbir 1365

Description: Exportation implication also converting head from biconditional to conditional. This proof is exbirVD in set.mm automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Assertion

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

Proof of Theorem exbir

Step	Hyp	Ref	Expression
1		bi2 189	. . 3 ⊢ ((χ ↔ θ) → (θ → χ))
2	1	imim2i 13	. 2 ⊢ (((φ ∧ ψ) → (χ ↔ θ)) → ((φ ∧ ψ) → (θ → χ)))
3	2	exp3a 425	1 ⊢ (((φ ∧ ψ) → (χ ↔ θ)) → (φ → (ψ → (θ → χ))))

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)