Theorem imp4d 575

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

Hypothesis

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

Assertion

Ref	Expression
imp4d	⊢ (φ → ((ψ ∧ (χ ∧ θ)) → τ))

Proof of Theorem imp4d

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4a 572	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → τ)))
3	2	imp3a 420	1 ⊢ (φ → ((ψ ∧ (χ ∧ θ)) → τ))

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:  imp45  580