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  662  pm2.67-2  718  oibabs  719  stdcn  852  pm2.85dc  910  peircedc  919  3jaob  1336  hbim  1591  hbimd  1619  i19.39  1686  hbae  1764  sbcof2  1856  sb4or  1879  tfi  4674  dmcosseq  4996  fliftfun  5926  tfrcl  6516  ac6sfi  7068  fsum2d  11961  fsumabs  11991  fsumiun  12003  fprod2d  12149  dvmptfsum  15414  bj-nnsn  16156  bj-pm2.18st  16173  setindis  16389  bdsetindis  16391