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Theorem adantlll 457
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 107 . 2  |-  ( ( ta  /\  ph )  ->  ph )
2 adantl2.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylanl1 388 1  |-  ( ( ( ( ta  /\  ph )  /\  ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem is referenced by:  fun11iun  5175  cnegexlem3  7251
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