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Theorem simp-9l 775
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-9l  |-  ( ( ( ( ( ( ( ( ( (
ph  /\  ps )  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  ->  ph )

Proof of Theorem simp-9l
StepHypRef Expression
1 simp-8l 773 . 2  |-  ( ( ( ( ( ( ( ( ( ph  /\ 
ps )  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  ->  ph )
21adantr 465 1  |-  ( ( ( ( ( ( ( ( ( (
ph  /\  ps )  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  ->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
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 371
This theorem is referenced by:  simp-10l  777  restutopopn  19940
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