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Theorem 3adant1r 1233
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 1206 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantlr 477 . 2  |-  ( ( ( ph  /\  ta )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1201 1  |-  ( ( ( ph  /\  ta )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982
This theorem is referenced by:  3adant2r  1235  3adant3r  1237  tfr1onlembacc  6427  tfr1onlembfn  6429  tfr1onlemaccex  6433  tfr1onlemres  6434  tfrcllembfn  6442  tfrcllemaccex  6446  tfrcllemres  6447  tfrcldm  6448  tfrcl  6449  mulassnqg  7496  prarloc  7615  prmuloc  7678  addasssrg  7868  axaddass  7984  ghmgrp  13425
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