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  3430  reupick  3434  po2nr  4327  fvmptt  5628  fliftfund  5819  f1ocnv2d  6098  addclpi  7356  addnidpig  7365  mulnqprl  7597  mulnqpru  7598  ltsubrp  9720  ltaddrp  9721  divgcdcoprm0  12133  infpnlem1  12391  imasgrp2  13052  imasrng  13310  imasring  13414  innei  14123  tgcnp  14169  isxmetd  14307