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Theorem mp2ani 698
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 696 . 2 (𝜑 → (𝜒𝜃))
51, 4mpi 20 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
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 207  df-an 396
This theorem is referenced by:  inf0  9661  dfom3  9687  dfac5lem4  10166  dfac5lem4OLD  10168  dfac9  10177  cflem  10285  cflemOLD  10286  canthp1lem2  10693  addsrpr  11115  mulsrpr  11116  trclublem  15034  gcdaddmlem  16561  tgjustf  28481  sto1i  32255  stji1i  32261  kur14lem9  35219  dfon2lem4  35787  rtrclex  43630  comptiunov2i  43719
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