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

Theorem bj-exlimmpbir 34114
 Description: Lemma for theorems of the vtoclg 3572 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpbir.nf 𝑥𝜑
bj-exlimmpbir.maj (𝜒 → (𝜑𝜓))
bj-exlimmpbir.min 𝜓
Assertion
Ref Expression
bj-exlimmpbir (∃𝑥𝜒𝜑)

Proof of Theorem bj-exlimmpbir
StepHypRef Expression
1 bj-exlimmpbir.nf . 2 𝑥𝜑
2 bj-exlimmpbir.min . . 3 𝜓
3 bj-exlimmpbir.maj . . 3 (𝜒 → (𝜑𝜓))
42, 3mpbiri 259 . 2 (𝜒𝜑)
51, 4exlimi 2210 1 (∃𝑥𝜒𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 207  ∃wex 1773  Ⅎwnf 1777 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-12 2169 This theorem depends on definitions:  df-bi 208  df-ex 1774  df-nf 1778 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator