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Theorem sylancl3 32403
Description: Shortens 11 proofs by a total of around 150 bytes. (Contributed by BJ, 25-Apr-2019.)
Hypotheses
Ref Expression
sylancl3.1  |-  ( ph  ->  ps )
sylancl3.2  |-  ch
sylancl3.3  |-  ( th  <->  ( ps  /\  ch )
)
Assertion
Ref Expression
sylancl3  |-  ( ph  ->  th )

Proof of Theorem sylancl3
StepHypRef Expression
1 sylancl3.1 . 2  |-  ( ph  ->  ps )
2 sylancl3.2 . 2  |-  ch
3 sylancl3.3 . . 3  |-  ( th  <->  ( ps  /\  ch )
)
43biimpri 206 . 2  |-  ( ( ps  /\  ch )  ->  th )
51, 2, 4sylancl 662 1  |-  ( ph  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator