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Theorem 3adant1r 1163
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
3adant1r  |-  ( ( ( ph  /\  ta )  /\  ps  /\  ch )  ->  th )

Proof of Theorem 3adant1r
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213expb 1140 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantlr 461 . 2  |-  ( ( ( ph  /\  ta )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1135 1  |-  ( ( ( ph  /\  ta )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  3adant2r  1165  3adant3r  1167  tfr1onlembacc  6011  tfr1onlembfn  6013  tfr1onlemaccex  6017  tfr1onlemres  6018  tfrcllembfn  6026  tfrcllemaccex  6030  tfrcllemres  6031  tfrcldm  6032  tfrcl  6033  mulassnqg  6688  prarloc  6807  prmuloc  6870  addasssrg  7047  axaddass  7152
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