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Theorem 3adant2l 1179
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 1158 . . 3  |-  ( ( ps  /\  ph  /\  ch )  ->  th )
323adant1l 1177 . 2  |-  ( ( ( ta  /\  ps )  /\  ph  /\  ch )  ->  th )
433com12 1158 1  |-  ( (
ph  /\  ( ta  /\ 
ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  axdc3lem4  8338  modexp  11519  lmmbr2  19217  nvaddsub4  22147  ax5seglem1  25872  ax5seglem2  25873  pellex  26912  athgt  30327  ltrncoelN  31014  ltrncoat  31015  trlcoabs  31592  tendoplcl2  31649  tendopltp  31651  dih1dimatlem0  32200
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939
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