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Theorem ad7antr 736
Description: Deduction adding 7 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypothesis
Ref Expression
ad2ant.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
ad7antr  |-  ( ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  ->  ps )

Proof of Theorem ad7antr
StepHypRef Expression
1 ad2ant.1 . . 3  |-  ( ph  ->  ps )
21ad6antr 734 . 2  |-  ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  ->  ps )
32adantr 463 1  |-  ( ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 369
This theorem is referenced by:  ad8antr  738  catpropd  15320  natpropd  15587  ucncn  21078  tgcgrxfr  24288  tgbtwnconn1lem3  24342  tgbtwnconn1  24343  midexlem  24452  lnopp2hpgb  24515  sigapildsys  28596  afsval  29048
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