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Theorem 3adant3r 1236
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
3adant3r  |-  ( (
ph  /\  ps  /\  ( ch  /\  ta ) )  ->  th )

Proof of Theorem 3adant3r
StepHypRef Expression
1 3adant1l.1 . . . 4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213com13 1209 . . 3  |-  ( ( ch  /\  ps  /\  ph )  ->  th )
323adant1r 1232 . 2  |-  ( ( ( ch  /\  ta )  /\  ps  /\  ph )  ->  th )
433com13 1209 1  |-  ( (
ph  /\  ps  /\  ( ch  /\  ta ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    /\ w3a 979
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 981
This theorem is referenced by:  addassnqg  7394  mulassnqg  7396  prarloc  7515  ltpopr  7607  ltexprlemfl  7621  ltexprlemfu  7623  addasssrg  7768  axaddass  7884  apmul1  8758  ltmul2  8826  lemul2  8827  dvdscmulr  11840  dvdsmulcr  11841  modremain  11947  ndvdsadd  11949  rpexp12i  12168  xblcntrps  14153  xblcntr  14154
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