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Theorem 3adant2r 1228
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
3adant2r  |-  ( (
ph  /\  ( ps  /\ 
ta )  /\  ch )  ->  th )

Proof of Theorem 3adant2r
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com12 1202 . . 3  |-  ( ( ps  /\  ph  /\  ch )  ->  th )
323adant1r 1226 . 2  |-  ( ( ( ps  /\  ta )  /\  ph  /\  ch )  ->  th )
433com12 1202 1  |-  ( (
ph  /\  ( ps  /\ 
ta )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 973
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 975
This theorem is referenced by:  caovimo  6044  mulassnqg  7339  prarloc  7458  ltexprlemfl  7564  ltexprlemfu  7566  addasssrg  7711  axaddass  7827
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