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Theorem mp2ani 423
Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mp2ani.1  |-  ps
mp2ani.2  |-  ch
mp2ani.3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
Assertion
Ref Expression
mp2ani  |-  ( ph  ->  th )

Proof of Theorem mp2ani
StepHypRef Expression
1 mp2ani.2 . 2  |-  ch
2 mp2ani.1 . . 3  |-  ps
3 mp2ani.3 . . 3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
42, 3mpani 421 . 2  |-  ( ph  ->  ( ch  ->  th )
)
51, 4mpi 15 1  |-  ( ph  ->  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 depends on definitions:  df-bi 115
This theorem is referenced by:  th3q  6377  addnnnq0  6987  mulnnnq0  6988  addsrpr  7270  mulsrpr  7271
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