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Theorem 3adant2l 1233
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 1208 . . 3  |-  ( ( ps  /\  ph  /\  ch )  ->  th )
323adant1l 1231 . 2  |-  ( ( ( ta  /\  ps )  /\  ph  /\  ch )  ->  th )
433com12 1208 1  |-  ( (
ph  /\  ( ta  /\ 
ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 981
This theorem is referenced by:  sbthlemi4  6976  addassnqg  7398  mulassnqg  7400  prmuloc  7582  ltpopr  7611  addasssrg  7772  axaddass  7888
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