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Theorem mpanr2 429
Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanr2.1  |-  ch
mpanr2.2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Assertion
Ref Expression
mpanr2  |-  ( (
ph  /\  ps )  ->  th )

Proof of Theorem mpanr2
StepHypRef Expression
1 mpanr2.1 . . 3  |-  ch
21jctr 308 . 2  |-  ( ps 
->  ( ps  /\  ch ) )
3 mpanr2.2 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
42, 3sylan2 280 1  |-  ( (
ph  /\  ps )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  op1steq  5857  pm54.43  6554  prarloclemarch2  6707  prarloclemlt  6781  prsradd  7060  muleqadd  7861  divdivap1  7914  addltmul  8370  elfzp1b  9226  elfzm1b  9227  expp1zap  9658  expm1ap  9659
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