Theorem impancom 427

Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013.)

Hypothesis

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

Assertion

Ref	Expression
impancom	⊢ ((φ ∧ χ) → (ψ → θ))

Proof of Theorem impancom

Step	Hyp	Ref	Expression
1		impancom.1	. . . 4 ⊢ ((φ ∧ ψ) → (χ → θ))
2	1	ex 423	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	com23 72	. 2 ⊢ (φ → (χ → (ψ → θ)))
4	3	imp 418	1 ⊢ ((φ ∧ χ) → (ψ → θ))

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:  spimt  1974  eqrdav  2352