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Theorem mp2ani 681
Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004.)
Hypotheses
Ref Expression
mp2ani.1 𝜓
mp2ani.2 𝜒
mp2ani.3 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
mp2ani (𝜑𝜃)

Proof of Theorem mp2ani
StepHypRef Expression
1 mp2ani.2 . 2 𝜒
2 mp2ani.1 . . 3 𝜓
3 mp2ani.3 . . 3 (𝜑 → ((𝜓𝜒) → 𝜃))
42, 3mpani 679 . 2 (𝜑 → (𝜒𝜃))
51, 4mpi 20 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 198  df-an 385
This theorem is referenced by:  dfom3  8794  dfac5lem4  9235  dfac9  9246  cflem  9356  canthp1lem2  9763  addsrpr  10184  mulsrpr  10185  trclublem  13962  gcdaddmlem  15467  sto1i  29429  stji1i  29435  kur14lem9  31524  dfon2lem4  32016  rtrclex  38425  comptiunov2i  38499
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