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Theorem xchbinxr 641
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchbinxr.1  |-  ( ph  <->  -. 
ps )
xchbinxr.2  |-  ( ch  <->  ps )
Assertion
Ref Expression
xchbinxr  |-  ( ph  <->  -. 
ch )

Proof of Theorem xchbinxr
StepHypRef Expression
1 xchbinxr.1 . 2  |-  ( ph  <->  -. 
ps )
2 xchbinxr.2 . . 3  |-  ( ch  <->  ps )
32bicomi 130 . 2  |-  ( ps  <->  ch )
41, 3xchbinx 640 1  |-  ( ph  <->  -. 
ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  xordc1  1325  sbnv  1810  ralnex  2359  difab  3240  disjsn  3462  iindif2m  3753  reldm0  4581
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