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Theorem bibi12i 321
Description: The equivalence of two equivalences. (Contributed by NM, 26-May-1993.)
Hypotheses
Ref Expression
bibi2i.1  |-  ( ph  <->  ps )
bibi12i.2  |-  ( ch  <->  th )
Assertion
Ref Expression
bibi12i  |-  ( (
ph 
<->  ch )  <->  ( ps  <->  th ) )

Proof of Theorem bibi12i
StepHypRef Expression
1 bibi12i.2 . . 3  |-  ( ch  <->  th )
21bibi2i 319 . 2  |-  ( (
ph 
<->  ch )  <->  ( ph  <->  th ) )
3 bibi2i.1 . . 3  |-  ( ph  <->  ps )
43bibi1i 320 . 2  |-  ( (
ph 
<->  th )  <->  ( ps  <->  th ) )
52, 4bitri 257 1  |-  ( (
ph 
<->  ch )  <->  ( ps  <->  th ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 190
This theorem is referenced by:  pm5.32  646  orbidi  948  pm5.7  950  xorbi12i  1431  abbi  2575  brsymdif  4472  nfnid  4642  asymref  5234  isocnv2  6246  zfcndrep  9064  f1omvdco3  17138  brtxpsd  30709  bj-sbeq  31547  rp-fakeoranass  36202  rp-fakeinunass  36204  relexp0eq  36337
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