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  1556  hbimd  1584  i19.39  1651  hbae  1729  sbcof2  1821  sb4or  1844  tfi  4614  dmcosseq  4933  fliftfun  5839  tfrcl  6417  ac6sfi  6954  fsum2d  11578  fsumabs  11608  fsumiun  11620  fprod2d  11766  bj-nnsn  15225  bj-pm2.18st  15242  setindis  15459  bdsetindis  15461