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Theorem prtlem50 26814
Description: Lemma for prter3 26853. (Contributed by Rodolfo Medina, 12-Oct-2010.)
Hypotheses
Ref Expression
prtlem50.1  |-  ( ph  ->  ( ps  ->  ch ) )
prtlem50.2  |-  ( th 
->  ta )
Assertion
Ref Expression
prtlem50  |-  ( ph  ->  ( ( ps  /\  th )  ->  ( ch  /\ 
ta ) ) )

Proof of Theorem prtlem50
StepHypRef Expression
1 prtlem50.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 prtlem50.2 . . 3  |-  ( th 
->  ta )
32a1i 10 . 2  |-  ( ph  ->  ( th  ->  ta ) )
41, 3anim12d 546 1  |-  ( ph  ->  ( ( ps  /\  th )  ->  ( ch  /\ 
ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
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  df-an 360
  Copyright terms: Public domain W3C validator