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Theorem 3adant1r 1192
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 1165 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32adantlr 466 . 2  |-  ( ( ( ph  /\  ta )  /\  ( ps  /\  ch ) )  ->  th )
433impb 1160 1  |-  ( ( ( ph  /\  ta )  /\  ps  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  3adant2r  1194  3adant3r  1196  tfr1onlembacc  6205  tfr1onlembfn  6207  tfr1onlemaccex  6211  tfr1onlemres  6212  tfrcllembfn  6220  tfrcllemaccex  6224  tfrcllemres  6225  tfrcldm  6226  tfrcl  6227  mulassnqg  7156  prarloc  7275  prmuloc  7338  addasssrg  7528  axaddass  7644
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