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  664  pm2.67-2  721  oibabs  722  stdcn  855  pm2.85dc  913  peircedc  922  3jaob  1339  hbim  1594  hbimd  1622  i19.39  1689  hbae  1766  sbcof2  1859  sb4or  1882  tfi  4709  dmcosseq  5034  fliftfun  5975  tfrcl  6608  ac6sfi  7168  fsum2d  12146  fsumabs  12176  fsumiun  12188  fprod2d  12334  dvmptfsum  15716  bj-nnsn  16631  bj-pm2.18st  16648  setindis  16863  bdsetindis  16865