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Theorem mp2ani 697
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 695 . 2 (𝜑 → (𝜒𝜃))
51, 4mpi 20 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397
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 206  df-an 398
This theorem is referenced by:  inf0  9616  dfom3  9642  dfac5lem4  10121  dfac9  10131  cflem  10241  canthp1lem2  10648  addsrpr  11070  mulsrpr  11071  trclublem  14942  gcdaddmlem  16465  tgjustf  27755  sto1i  31520  stji1i  31526  kur14lem9  34236  dfon2lem4  34789  rtrclex  42416  comptiunov2i  42505
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