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Theorem 3adant2l 1164
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
3adant2l  |-  ( (
ph  /\  ( ta  /\ 
ps )  /\  ch )  ->  th )

Proof of Theorem 3adant2l
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com12 1143 . . 3  |-  ( ( ps  /\  ph  /\  ch )  ->  th )
323adant1l 1162 . 2  |-  ( ( ( ta  /\  ps )  /\  ph  /\  ch )  ->  th )
433com12 1143 1  |-  ( (
ph  /\  ( ta  /\ 
ps )  /\  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  6686  mulassnqg  6688  prmuloc  6870  ltpopr  6899  addasssrg  7047  axaddass  7152
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