Theorem imp4a 572

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

Hypothesis

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

Assertion

Ref	Expression
imp4a	⊢ (φ → (ψ → ((χ ∧ θ) → τ)))

Proof of Theorem imp4a

Step	Hyp	Ref	Expression
1		imp4.1	. 2 ⊢ (φ → (ψ → (χ → (θ → τ))))
2		impexp 433	. 2 ⊢ (((χ ∧ θ) → τ) ↔ (χ → (θ → τ)))
3	1, 2	syl6ibr 218	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:  imp4b  573  imp4d  575  imp55  584  imp511  585  reuss2  3536