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Theorem 3ad2antl3 1156
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 473 . 2  |-  ( ( ( ta  /\  ph )  /\  ch )  ->  th )
323adantl1 1148 1  |-  ( ( ( ps  /\  ta  /\ 
ph )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 973
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 975
This theorem is referenced by:  rspc3ev  2851  brcogw  4780  cocan1  5766  ov6g  5990  prarloclemarch2  7381  ltpopr  7557  ltsopr  7558  zdivmul  9302  lcmdvds  12033
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