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Theorem adantl3r 747
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.)
Hypothesis
Ref Expression
adantl3r.1  |-  ( ( ( ( ph  /\  rh )  /\  mu )  /\  la )  ->  ka )
Assertion
Ref Expression
adantl3r  |-  ( ( ( ( ( ph  /\ 
si )  /\  rh )  /\  mu )  /\  la )  ->  ka )

Proof of Theorem adantl3r
StepHypRef Expression
1 adantl3r.1 . . . 4  |-  ( ( ( ( ph  /\  rh )  /\  mu )  /\  la )  ->  ka )
21ex 432 . . 3  |-  ( ( ( ph  /\  rh )  /\  mu )  -> 
( la  ->  ka )
)
32adantllr 716 . 2  |-  ( ( ( ( ph  /\  si )  /\  rh )  /\  mu )  -> 
( la  ->  ka )
)
43imp 427 1  |-  ( ( ( ( ( ph  /\ 
si )  /\  rh )  /\  mu )  /\  la )  ->  ka )
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:  adantl4r  748  legov  24173  omssubadd  28508  adantlllr  31656  ad5ant1345  33635
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