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Theorem 3adant1r 1234
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 1207 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantlr 477 . 2  |-  ( ( ( ph  /\  ta )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1202 1  |-  ( ( ( ph  /\  ta )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 981
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 983
This theorem is referenced by:  3adant2r  1236  3adant3r  1238  tfr1onlembacc  6428  tfr1onlembfn  6430  tfr1onlemaccex  6434  tfr1onlemres  6435  tfrcllembfn  6443  tfrcllemaccex  6447  tfrcllemres  6448  tfrcldm  6449  tfrcl  6450  mulassnqg  7497  prarloc  7616  prmuloc  7679  addasssrg  7869  axaddass  7985  ghmgrp  13454
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