Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  exlimii Structured version   Visualization version   GIF version

Theorem exlimii 32006
 Description: Inference associated with exlimi 2073. Inferring a theorem when it is implied by an antecedent which may be true. (Contributed by BJ, 15-Sep-2018.)
Hypotheses
Ref Expression
exlimii.1 𝑥𝜓
exlimii.2 (𝜑𝜓)
exlimii.3 𝑥𝜑
Assertion
Ref Expression
exlimii 𝜓

Proof of Theorem exlimii
StepHypRef Expression
1 exlimii.3 . 2 𝑥𝜑
2 exlimii.1 . . 3 𝑥𝜓
3 exlimii.2 . . 3 (𝜑𝜓)
42, 3exlimi 2073 . 2 (∃𝑥𝜑𝜓)
51, 4ax-mp 5 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1695  Ⅎwnf 1699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-or 384  df-ex 1696  df-nf 1701 This theorem is referenced by:  exlimiieq1  32009  exlimiieq2  32010
 Copyright terms: Public domain W3C validator