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Theorem mpanlr1 431
Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanlr1.1  |-  ps
mpanlr1.2  |-  ( ( ( ph  /\  ( ps  /\  ch ) )  /\  th )  ->  ta )
Assertion
Ref Expression
mpanlr1  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )

Proof of Theorem mpanlr1
StepHypRef Expression
1 mpanlr1.1 . . 3  |-  ps
21jctl 307 . 2  |-  ( ch 
->  ( ps  /\  ch ) )
3 mpanlr1.2 . 2  |-  ( ( ( ph  /\  ( ps  /\  ch ) )  /\  th )  ->  ta )
42, 3sylanl2 395 1  |-  ( ( ( ph  /\  ch )  /\  th )  ->  ta )
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: (None)
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