Theorem imp5a 581

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

Hypothesis

Ref	Expression
imp5.1	⊢ (φ → (ψ → (χ → (θ → (τ → η)))))

Assertion

Ref	Expression
imp5a	⊢ (φ → (ψ → (χ → ((θ ∧ τ) → η))))

Proof of Theorem imp5a

Step	Hyp	Ref	Expression
1		imp5.1	. 2 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))
2		pm3.31 432	. 2 ⊢ ((θ → (τ → η)) → ((θ ∧ τ) → η))
3	1, 2	syl8 65	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: (None)