Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-exlimmpi Structured version   Visualization version   GIF version

Theorem bj-exlimmpi 31929
Description: Lemma for bj-vtoclg1f1 31934 (an instance of this lemma is a version of bj-vtoclg1f1 31934 where 𝑥 and 𝑦 are identified). (Contributed by BJ, 30-Apr-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpi.nf 𝑥𝜓
bj-exlimmpi.maj (𝜒 → (𝜑𝜓))
bj-exlimmpi.min 𝜑
Assertion
Ref Expression
bj-exlimmpi (∃𝑥𝜒𝜓)

Proof of Theorem bj-exlimmpi
StepHypRef Expression
1 bj-exlimmpi.nf . 2 𝑥𝜓
2 bj-exlimmpi.min . . 3 𝜑
3 bj-exlimmpi.maj . . 3 (𝜒 → (𝜑𝜓))
42, 3mpi 20 . 2 (𝜒𝜓)
51, 4exlimi 2043 1 (∃𝑥𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1694  wnf 1698
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-12 1983
This theorem depends on definitions:  df-bi 195  df-ex 1695  df-nf 1699
This theorem is referenced by:  bj-vtoclg1f1  31934  bj-vtoclg1f  31935  bj-vtoclg1fv  31936
  Copyright terms: Public domain W3C validator