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Theorem ad4ant134 1206
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad4ant3.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
ad4ant134  |-  ( ( ( ( ph  /\  ta )  /\  ps )  /\  ch )  ->  th )

Proof of Theorem ad4ant134
StepHypRef Expression
1 ad4ant3.1 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expa 1192 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
32adantllr 473 1  |-  ( ( ( ( ph  /\  ta )  /\  ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 967
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 969
This theorem is referenced by: (None)
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