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Theorem adantl6r 23912
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)
Hypothesis
Ref Expression
adantl6r.1  |-  ( ( ( ( ( ( ( ph  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  /\  la )  ->  ka )
Assertion
Ref Expression
adantl6r  |-  ( ( ( ( ( ( ( ( ph  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  /\  la )  ->  ka )

Proof of Theorem adantl6r
StepHypRef Expression
1 adantl6r.1 . . . 4  |-  ( ( ( ( ( ( ( ph  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  /\  la )  ->  ka )
21ex 424 . . 3  |-  ( ( ( ( ( (
ph  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  ->  ( la  ->  ka ) )
32adantl5r 23911 . 2  |-  ( ( ( ( ( ( ( ph  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  ->  ( la  ->  ka ) )
43imp 419 1  |-  ( ( ( ( ( ( ( ( ph  /\  ta )  /\  et )  /\  ze )  /\  si )  /\  rh )  /\  mu )  /\  la )  ->  ka )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  pstmxmet  24245
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 178  df-an 361
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