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Theorem e3bir 28185
Description: Right biconditional form of e3 28183. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e3bir.1  |-  (. ph ,. ps ,. ch  ->.  th ).
e3bir.2  |-  ( ta  <->  th )
Assertion
Ref Expression
e3bir  |-  (. ph ,. ps ,. ch  ->.  ta ).

Proof of Theorem e3bir
StepHypRef Expression
1 e3bir.1 . 2  |-  (. ph ,. ps ,. ch  ->.  th ).
2 e3bir.2 . . 3  |-  ( ta  <->  th )
32biimpri 198 . 2  |-  ( th 
->  ta )
41, 3e3 28183 1  |-  (. ph ,. ps ,. ch  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    <-> wb 177   (.wvd3 28013
This theorem is referenced by:  en3lplem2VD  28290
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-vd3 28016
  Copyright terms: Public domain W3C validator