Theorem exp4a 589

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

Hypothesis

Ref	Expression
exp4a.1	⊢ (φ → (ψ → ((χ ∧ θ) → τ)))

Assertion

Ref	Expression
exp4a	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp4a

Step	Hyp	Ref	Expression
1		exp4a.1	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → τ)))
2		impexp 433	. 2 ⊢ (((χ ∧ θ) → τ) ↔ (χ → (θ → τ)))
3	1, 2	syl6ib 217	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:  exp4b  590  exp4d  592  exp45  597  exp5c  599  spfininduct  4541  fununiq  5518  fntxp  5805