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Theorem 3adantr1 1125
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
Hypothesis
Ref Expression
3adantr.1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Assertion
Ref Expression
3adantr1  |-  ( (
ph  /\  ( ta  /\ 
ps  /\  ch )
)  ->  th )

Proof of Theorem 3adantr1
StepHypRef Expression
1 3simpc 965 . 2  |-  ( ( ta  /\  ps  /\  ch )  ->  ( ps 
/\  ch ) )
2 3adantr.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylan2 284 1  |-  ( (
ph  /\  ( ta  /\ 
ps  /\  ch )
)  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
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 949
This theorem is referenced by:  3ad2antr3  1133  3adant3r1  1175  swopo  4198  isosolem  5693  caovlem2d  5931  divmuldivap  8440
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