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  660  pm2.67-2  715  oibabs  716  stdcn  849  pm2.85dc  907  peircedc  916  3jaob  1315  hbim  1568  hbimd  1596  i19.39  1663  hbae  1741  sbcof2  1833  sb4or  1856  tfi  4630  dmcosseq  4950  fliftfun  5865  tfrcl  6450  ac6sfi  6995  fsum2d  11746  fsumabs  11776  fsumiun  11788  fprod2d  11934  dvmptfsum  15197  bj-nnsn  15669  bj-pm2.18st  15686  setindis  15903  bdsetindis  15905