Theorem imp55 584

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
imp55	⊢ (((φ ∧ (ψ ∧ (χ ∧ θ))) ∧ τ) → η)

Proof of Theorem imp55

Step	Hyp	Ref	Expression
1		imp5.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → (τ → η)))))
2	1	imp4a 572	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → (τ → η))))
3	2	imp42 577	1 ⊢ (((φ ∧ (ψ ∧ (χ ∧ θ))) ∧ τ) → η)

This proof depends on syntax axioms:   → wi 4   ∧ 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)