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Theorem adantlll 472
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 2-Dec-2012.)
Hypothesis
Ref Expression
adantl2.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
adantlll  |-  ( ( ( ( ta  /\  ph )  /\  ps )  /\  ch )  ->  th )

Proof of Theorem adantlll
StepHypRef Expression
1 simpr 109 . 2  |-  ( ( ta  /\  ph )  ->  ph )
2 adantl2.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylanl1 400 1  |-  ( ( ( ( ta  /\  ph )  /\  ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
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 is referenced by:  ad4ant23  507  ad4ant24  508  ad4ant234  1207  fun11iun  5448  fiintim  6886  cnegexlem3  8067  bezoutlemzz  11924  cnptopco  12789
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