Theorem exp45 597

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

Hypothesis

Ref	Expression
exp45.1	⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → τ)

Assertion

Ref	Expression
exp45	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp45

Step	Hyp	Ref	Expression
1		exp45.1	. . 3 ⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → τ)
2	1	exp32 588	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → τ)))
3	2	exp4a 589	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: (None)