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Theorem mpan2i 697
Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994.) (Proof shortened by Wolf Lammen, 19-Nov-2012.)
Hypotheses
Ref Expression
mpan2i.1 𝜒
mpan2i.2 (𝜑 → ((𝜓𝜒) → 𝜃))
Assertion
Ref Expression
mpan2i (𝜑 → (𝜓𝜃))

Proof of Theorem mpan2i
StepHypRef Expression
1 mpan2i.1 . . 3 𝜒
21a1i 11 . 2 (𝜑𝜒)
3 mpan2i.2 . 2 (𝜑 → ((𝜓𝜒) → 𝜃))
42, 3mpan2d 694 1 (𝜑 → (𝜓𝜃))
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:  tcwf  9923  cflecard  10293  01sqrexlem7  15287  setciso  18136  lsmss1  19683  rngciso  20638  ringciso  20672  sincosq1lem  26539  pjcompi  31691  mdsl1i  32340  dfon2lem3  35786  dfon2lem7  35790  tan2h  37619  dvasin  37711  ismrc  42712  nnsum4primes4  47776  nnsum4primesprm  47778  nnsum4primesgbe  47780  nnsum4primesle9  47782  rngcisoALTV  48193  ringcisoALTV  48227  aacllem  49320
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