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Theorem 3adant1l 1177
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
3adant1l  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )

Proof of Theorem 3adant1l
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expb 1155 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantll 696 . 2  |-  ( ( ( ta  /\  ph )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1150 1  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
This theorem is referenced by:  3adant2l  1179  3adant3l  1181  cfsmolem  8155  axdc3lem4  8338  spwpr4  14668  issubmnd  14729  restnlly  17550  hasheuni  24480  pellex  26912  mendlmod  27492
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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