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Theorem ee3bir 27637
Description: Right-biconditional form of e3 27885 without virtual deduction connectives. Special theorem needed for Alan Sare's virtual deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee3bir.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
ee3bir.2  |-  ( ta  <->  th )
Assertion
Ref Expression
ee3bir  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )

Proof of Theorem ee3bir
StepHypRef Expression
1 ee3bir.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 ee3bir.2 . . 3  |-  ( ta  <->  th )
32biimpri 197 . 2  |-  ( th 
->  ta )
41, 3syl8 65 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176
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 177
  Copyright terms: Public domain W3C validator