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Theorem sbid2 2133
Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sbid2.1  |-  F/ x ph
Assertion
Ref Expression
sbid2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )

Proof of Theorem sbid2
StepHypRef Expression
1 sbco 2132 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
2 sbid2.1 . . 3  |-  F/ x ph
32sbf 2075 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
41, 3bitri 241 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177   F/wnf 1550   [wsb 1655
This theorem is referenced by:  sbco2  2135  sb5rf  2139  sb6rf  2140  sbid2v  2173
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656
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