Theorem imp32 257

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 254	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
3	2	imp 124	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem is referenced by:  imp42  354  impr  379  anasss  399  an13s  567  3expb  1206  reuss2  3444  reupick  3448  po2nr  4345  fvmptt  5656  fliftfund  5847  f1ocnv2d  6131  addclpi  7411  addnidpig  7420  mulnqprl  7652  mulnqpru  7653  ltsubrp  9782  ltaddrp  9783  divgcdcoprm0  12294  infpnlem1  12553  imasmnd2  13154  imasgrp2  13316  imasrng  13588  imasring  13696  innei  14483  tgcnp  14529  isxmetd  14667  2lgslem1a1  15411