Theorem exp42 594

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

Hypothesis

Ref	Expression
exp42.1	⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)

Assertion

Ref	Expression
exp42	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp42

Step	Hyp	Ref	Expression
1		exp42.1	. . 3 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)
2	1	exp31 587	. 2 ⊢ (φ → ((ψ ∧ χ) → (θ → τ)))
3	2	exp3a 425	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:  f1o2d  5728