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Theorem ee22 1352
Description: Virtual deduction rule e22 27723 without virtual deduction connectives. Special theorem needed for Alan Sare's virtual deduction translation tool. (Contributed by Alan Sare, 2-May-2011.) (New usage is discouraged.) TODO: decide if this is worth keeping.
Hypotheses
Ref Expression
ee22.1  |-  ( ph  ->  ( ps  ->  ch ) )
ee22.2  |-  ( ph  ->  ( ps  ->  th )
)
ee22.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
ee22  |-  ( ph  ->  ( ps  ->  ta ) )

Proof of Theorem ee22
StepHypRef Expression
1 ee22.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 ee22.2 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 ee22.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
41, 2, 3syl6c 60 1  |-  ( ph  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  ee21  1365  ee33  27567  sb5ALT  27571  tratrb  27582  onfrALT  27597  a9e2ndeq  27608  ee22an  27725  sspwtrALT  27876  sspwtrALT2  27877  pwtrOLD  27879  pwtrrOLD  27881  trintALT  27937
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator