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Theorem 3adant1l 1174
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 1152 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantll 694 . 2  |-  ( ( ( ta  /\  ph )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1147 1  |-  ( ( ( ta  /\  ph )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    /\ w3a 934
This theorem is referenced by:  3adant2l  1176  3adant3l  1178  cfsmolem  7912  axdc3lem4  8095  spwpr4  14356  issubmnd  14417  restnlly  17224  hasheuni  23468  pellex  27023  mendlmod  27604
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
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