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Theorem 3adant3l 1195
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 1169 . . 3  |-  ( ( ch  /\  ps  /\  ph )  ->  th )
323adant1l 1191 . 2  |-  ( ( ( ta  /\  ch )  /\  ps  /\  ph )  ->  th )
433com13 1169 1  |-  ( (
ph  /\  ps  /\  ( ta  /\  ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 945
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 947
This theorem is referenced by:  addassnqg  7154  mulassnqg  7156  prarloc  7275  prmuloc  7338  addasssrg  7528  axaddass  7644
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