Theorem exp43 595

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp43.1	⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)

Assertion

Ref	Expression
exp43	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp43

Step	Hyp	Ref	Expression
1		exp43.1	. . 3 ⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)
2	1	ex 423	. 2 ⊢ ((φ ∧ ψ) → ((χ ∧ θ) → τ))
3	2	exp4b 590	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

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:  exp53  600  funssres  5145