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Theorem mp2ani 695
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 693 . 2 (𝜑 → (𝜒𝜃))
51, 4mpi 20 1 (𝜑𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 397
This theorem is referenced by:  inf0  9379  dfom3  9405  dfac5lem4  9882  dfac9  9892  cflem  10002  canthp1lem2  10409  addsrpr  10831  mulsrpr  10832  trclublem  14706  gcdaddmlem  16231  tgjustf  26834  sto1i  30598  stji1i  30604  kur14lem9  33176  dfon2lem4  33762  rtrclex  41225  comptiunov2i  41314
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