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Theorem 3adantl1 1095
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
3adantl1  |-  ( ( ( ta  /\  ph  /\ 
ps )  /\  ch )  ->  th )

Proof of Theorem 3adantl1
StepHypRef Expression
1 3simpc 938 . 2  |-  ( ( ta  /\  ph  /\  ps )  ->  ( ph  /\ 
ps ) )
2 3adantl.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylan 277 1  |-  ( ( ( ta  /\  ph  /\ 
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:  3ad2antl2  1102  3ad2antl3  1103  distrlem1prl  6834  distrlem1pru  6835  divmuldivap  7867  modqaddmulmod  9473  expnlbnd  9694  lcmledvds  10596
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