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  658  pm2.67-2  713  oibabs  714  stdcn  847  pm2.85dc  905  peircedc  914  3jaob  1302  hbim  1545  hbimd  1573  i19.39  1640  hbae  1718  sbcof2  1810  sb4or  1833  tfi  4581  dmcosseq  4898  fliftfun  5796  tfrcl  6364  ac6sfi  6897  fsum2d  11442  fsumabs  11472  fsumiun  11484  fprod2d  11630  bj-nnsn  14455  bj-pm2.18st  14472  setindis  14689  bdsetindis  14691