Theorem impr 602

Description: Import a wff into a right conjunct. (Contributed by Jeff Hankins, 30-Aug-2009.)

Hypothesis

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

Assertion

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

Proof of Theorem impr

Step	Hyp	Ref	Expression
1		impr.1	. . 3 ⊢ ((φ ∧ ψ) → (χ → θ))
2	1	ex 423	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp32 422	1 ⊢ ((φ ∧ (ψ ∧ χ)) → 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:  moi2  3017  preq12bg  4128  prepeano4  4451  f1o2d  5727  fndmeng  6046  enprmaplem3  6078  nchoicelem4  6292  fnfrec  6320