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  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  4583  dmcosseq  4900  fliftfun  5799  tfrcl  6367  ac6sfi  6900  fsum2d  11445  fsumabs  11475  fsumiun  11487  fprod2d  11633  bj-nnsn  14524  bj-pm2.18st  14541  setindis  14758  bdsetindis  14760