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Theorem 3adant3l 1166
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3adant3l  |-  ( (
ph  /\  ps  /\  ( ta  /\  ch ) )  ->  th )

Proof of Theorem 3adant3l
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com13 1144 . . 3  |-  ( ( ch  /\  ps  /\  ph )  ->  th )
323adant1l 1162 . 2  |-  ( ( ( ta  /\  ch )  /\  ps  /\  ph )  ->  th )
433com13 1144 1  |-  ( (
ph  /\  ps  /\  ( ta  /\  ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  addassnqg  6634  mulassnqg  6636  prarloc  6755  prmuloc  6818  addasssrg  6995  axaddass  7100
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