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

Theorem bj-exlimmpi 12904
Description: Lemma for bj-vtoclgf 12910. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmp.nf 𝑥𝜓
bj-exlimmp.min (𝜒𝜑)
bj-exlimmpi.maj (𝜒 → (𝜑𝜓))
Assertion
Ref Expression
bj-exlimmpi (∃𝑥𝜒𝜓)

Proof of Theorem bj-exlimmpi
StepHypRef Expression
1 bj-exlimmp.nf . 2 𝑥𝜓
2 bj-exlimmp.min . . 3 (𝜒𝜑)
3 bj-exlimmpi.maj . . 3 (𝜒 → (𝜑𝜓))
42, 3mpd 13 . 2 (𝜒𝜓)
51, 4exlimi 1558 1 (∃𝑥𝜒𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1421  wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-gen 1410  ax-ie2 1455  ax-4 1472
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator