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Theorem 3adantl2 1061
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
3adantl2  |-  ( ( ( ph  /\  ta  /\ 
ps )  /\  ch )  ->  th )

Proof of Theorem 3adantl2
StepHypRef Expression
1 3simpb 902 . 2  |-  ( (
ph  /\  ta  /\  ps )  ->  ( ph  /\  ps ) )
2 3adantl.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylan 267 1  |-  ( ( ( ph  /\  ta  /\ 
ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97    /\ w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  3ad2antl1  1066  nnmord  6090  ltaprg  6717  lediv2a  7861  zdiv  8328
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