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	|- ( ph -> ps )

Assertion

Ref	Expression
imim1i	|- ( ( ps -> ch ) -> ( ph -> ch ) )

Proof of Theorem imim1i

Step	Hyp	Ref	Expression
1		imim1i.1	. 2 |- ( ph -> ps )
2		id 19	. 2 |- ( ch -> ch )
3	1, 2	imim12i 59	1 |- ( ( ps -> ch ) -> ( ph -> ch ) )

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  4619  dmcosseq  4938  fliftfun  5846  tfrcl  6431  ac6sfi  6968  fsum2d  11617  fsumabs  11647  fsumiun  11659  fprod2d  11805  dvmptfsum  15045  bj-nnsn  15463  bj-pm2.18st  15480  setindis  15697  bdsetindis  15699