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Theorem ad7antr 718
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 716 . 2  |-  ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  ->  ps )
32adantr 451 1  |-  ( ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  ad8antr  720  catpropd  13628  natpropd  13866
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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