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Theorem 3adantlr3 31371
Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypothesis
Ref Expression
3adantlr3.1  |-  ( ( ( ph  /\  ( ps  /\  ch ) )  /\  th )  ->  ta )
Assertion
Ref Expression
3adantlr3  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  ta )

Proof of Theorem 3adantlr3
StepHypRef Expression
1 simpll 753 . 2  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  ph )
2 simplr1 1039 . . 3  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  ps )
3 simplr2 1040 . . 3  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  ch )
42, 3jca 532 . 2  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  ( ps  /\  ch ) )
5 simpr 461 . 2  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  th )
6 3adantlr3.1 . 2  |-  ( ( ( ph  /\  ( ps  /\  ch ) )  /\  th )  ->  ta )
71, 4, 5, 6syl21anc 1228 1  |-  ( ( ( ph  /\  ( ps  /\  ch  /\  et ) )  /\  th )  ->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    /\ w3a 974
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  df-3an 976
This theorem is referenced by:  fourierdlem42  31820
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