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Theorem mp2ani 659
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 657 . 2  |-  ( ph  ->  ( ch  ->  th )
)
51, 4mpi 16 1  |-  ( ph  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  th3q  6767  dfom3  7348  dfac5lem4  7753  dfac9  7762  cflem  7872  canthp1lem2  8275  gcdaddmlem  12707  sto1i  22816  stji1i  22822  kur14lem9  23745  dfon2lem4  24142
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator