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

Theorem bj-vtocl 34357
Description: Remove dependency on ax-ext 2773, df-clab 2780 and df-cleq 2794 (and df-sb 2070 and df-v 3446) from vtocl 3510. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-vtocl.s 𝐴𝑉
bj-vtocl.maj (𝑥 = 𝐴 → (𝜑𝜓))
bj-vtocl.min 𝜑
Assertion
Ref Expression
bj-vtocl 𝜓
Distinct variable groups:   𝑥,𝐴   𝜓,𝑥   𝑥,𝑉
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bj-vtocl
StepHypRef Expression
1 nfv 1915 . 2 𝑥𝜓
2 bj-vtocl.s . 2 𝐴𝑉
3 bj-vtocl.maj . 2 (𝑥 = 𝐴 → (𝜑𝜓))
4 bj-vtocl.min . 2 𝜑
51, 2, 3, 4bj-vtoclf 34356 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209   = wceq 1538  wcel 2112
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-12 2176
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-clel 2873
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator