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Theorem ad5ant1345 28636
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant1345.1  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
ad5ant1345  |-  ( ( ( ( ( ph  /\  et )  /\  ps )  /\  ch )  /\  th )  ->  ta )

Proof of Theorem ad5ant1345
StepHypRef Expression
1 ad5ant1345.1 . . . 4  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
21exp41 595 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
32adantr 453 . 2  |-  ( (
ph  /\  et )  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
43imp41 578 1  |-  ( ( ( ( ( ph  /\  et )  /\  ps )  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
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 179  df-an 362
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