Theorem imp45 580

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

Hypothesis

Ref	Expression
imp4.1	⊢ (φ → (ψ → (χ → (θ → τ))))

Assertion

Ref	Expression
imp45	⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → τ)

Proof of Theorem imp45

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4d 575	. 2 ⊢ (φ → ((ψ ∧ (χ ∧ θ)) → τ))
3	2	imp 418	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: (None)