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Theorem 3adantr3 1158
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
3adantr3  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  ta )
)  ->  th )

Proof of Theorem 3adantr3
StepHypRef Expression
1 3simpa 994 . 2  |-  ( ( ps  /\  ch  /\  ta )  ->  ( ps 
/\  ch ) )
2 3adantr.1 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
31, 2sylan2 286 1  |-  ( (
ph  /\  ( ps  /\ 
ch  /\  ta )
)  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 980
This theorem is referenced by:  3ad2antr1  1162  3ad2antr2  1163  3adant3r3  1214  isosolem  5824  caovlem2d  6066  tanaddap  11742  mhmmnd  12934  isxmet2d  13741  xmetres2  13772  comet  13892  xmetxp  13900
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