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Theorem ad4ant13 28518
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad4ant13.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
ad4ant13  |-  ( ( ( ( ph  /\  th )  /\  ps )  /\  ta )  ->  ch )

Proof of Theorem ad4ant13
StepHypRef Expression
1 ad4ant13.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 423 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32a1i24 26305 . 2  |-  ( ph  ->  ( th  ->  ( ps  ->  ( ta  ->  ch ) ) ) )
43imp41 576 1  |-  ( ( ( ( ph  /\  th )  /\  ps )  /\  ta )  ->  ch )
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
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