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Theorem 3ad2antl3 1146
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
3ad2antl3  |-  ( ( ( ps  /\  ta  /\ 
ph )  /\  ch )  ->  th )

Proof of Theorem 3ad2antl3
StepHypRef Expression
1 3ad2antl.1 . . 3  |-  ( (
ph  /\  ch )  ->  th )
21adantll 468 . 2  |-  ( ( ( ta  /\  ph )  /\  ch )  ->  th )
323adantl1 1138 1  |-  ( ( ( ps  /\  ta  /\ 
ph )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  rspc3ev  2833  brcogw  4757  cocan1  5739  ov6g  5960  prarloclemarch2  7341  ltpopr  7517  ltsopr  7518  zdivmul  9259  lcmdvds  11971
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