Theorem imim1i 60

Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 4-Aug-2012.)

Hypothesis

Ref	Expression
imim1i.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
imim1i	⊢ ((𝜓 → 𝜒) → (𝜑 → 𝜒))

Proof of Theorem imim1i

Step	Hyp	Ref	Expression
1		imim1i.1	. 2 ⊢ (𝜑 → 𝜓)
2		id 19	. 2 ⊢ (𝜒 → 𝜒)
3	1, 2	imim12i 59	1 ⊢ ((𝜓 → 𝜒) → (𝜑 → 𝜒))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  jarr  97  bi3ant  224  pm3.41  331  pm3.42  332  jarl  659  pm2.67-2  714  oibabs  715  stdcn  848  pm2.85dc  906  peircedc  915  3jaob  1313  hbim  1559  hbimd  1587  i19.39  1654  hbae  1732  sbcof2  1824  sb4or  1847  tfi  4618  dmcosseq  4937  fliftfun  5843  tfrcl  6422  ac6sfi  6959  fsum2d  11600  fsumabs  11630  fsumiun  11642  fprod2d  11788  dvmptfsum  14961  bj-nnsn  15379  bj-pm2.18st  15396  setindis  15613  bdsetindis  15615