Theorem imp32 422

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

Hypothesis

Ref	Expression
imp3.1	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
imp32	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Proof of Theorem imp32

Step	Hyp	Ref	Expression
1		imp3.1	. . 3 ⊢ (φ → (ψ → (χ → θ)))
2	1	imp3a 420	. 2 ⊢ (φ → ((ψ ∧ χ) → θ))
3	2	imp 418	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:  imp42  577  impr  602  anasss  628  an13s  778  3expb  1152  reuss2  3536  reupick  3540  tfinnn  4535  f1o2d  5728