MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ee22 Unicode version

Theorem ee22 1358
Description: Virtual deduction rule e22 27576 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 62 1  |-  ( ph  ->  ( ps  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  ee21  1371  ee33  27420  sb5ALT  27424  tratrb  27435  onfrALT  27450  a9e2ndeq  27461  ee22an  27578  sspwtrALT  27729  sspwtrALT2  27730  pwtrOLD  27732  pwtrrOLD  27734  trintALT  27790
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10
  Copyright terms: Public domain W3C validator