Theorem imp32 244

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	impd 242	. 2 ⊢ (φ → ((ψ ∧ χ) → θ))
3	2	imp 115	1 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Syntax hints:   → wi 4   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem is referenced by:  imp42  336  impr  361  anasss  379  an13s  501  3expb  1104  reuss2  3211  reupick  3215  po2nr  4037  fvmptt  5205  fliftfund  5380  f1ocnv2d  5646  addclpi  6311  addnidpig  6320  mulnqprl  6549  mulnqpru  6550  ltsubrp  8392  ltaddrp  8393