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Theorem sbid2 2244
Description: An identity law for substitution. (Contributed by NM, 14-May-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 2243 . 2  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  [ y  /  x ] ph )
2 sbid2.1 . . 3  |-  F/ x ph
32sbf 2211 . 2  |-  ( [ y  /  x ] ph 
<-> 
ph )
41, 3bitri 253 1  |-  ( [ y  /  x ] [ x  /  y ] ph  <->  ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 188   F/wnf 1669   [wsb 1799
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-12 1935  ax-13 2093
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-ex 1666  df-nf 1670  df-sb 1800
This theorem is referenced by:  sbtrt  2251  sbid2v  2288
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