Theorem exp5c 599

Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)

Hypothesis

Ref	Expression
exp5c.1	⊢ (φ → ((ψ ∧ χ) → ((θ ∧ τ) → η)))

Assertion

Ref	Expression
exp5c	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Proof of Theorem exp5c

Step	Hyp	Ref	Expression
1		exp5c.1	. . 3 ⊢ (φ → ((ψ ∧ χ) → ((θ ∧ τ) → η)))
2	1	exp4a 589	. 2 ⊢ (φ → ((ψ ∧ χ) → (θ → (τ → η))))
3	2	exp3a 425	1 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Syntax hints:   → wi 4   ∧ 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:  ssfin  4471