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Theorem 3bitr2ri 274
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitr2i.1  |-  ( ph  <->  ps )
3bitr2i.2  |-  ( ch  <->  ps )
3bitr2i.3  |-  ( ch  <->  th )
Assertion
Ref Expression
3bitr2ri  |-  ( th  <->  ph )

Proof of Theorem 3bitr2ri
StepHypRef Expression
1 3bitr2i.1 . . 3  |-  ( ph  <->  ps )
2 3bitr2i.2 . . 3  |-  ( ch  <->  ps )
31, 2bitr4i 252 . 2  |-  ( ph  <->  ch )
4 3bitr2i.3 . 2  |-  ( ch  <->  th )
53, 4bitr2i 250 1  |-  ( th  <->  ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184
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 185
This theorem is referenced by:  sbnf2OLD  2167  ssrab  3578  copsex2gb  5113  relop  5153  dmopab3  5215  issref  5380  fununi  5654  dffv2  5940  dfsup2  7902  kmlem3  8532  recmulnq  9342  ovoliunlem1  21676  shne0i  26070  ssiun3  27127  cnvoprab  27246  ind1a  27702  bnj1304  32975  bnj1253  33170  dalem20  34507
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