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Theorem bj-vtocl 36303
Description: Remove dependency on ax-ext 2697, df-clab 2704 and df-cleq 2718 (and df-sb 2060 and df-v 3470) from vtocl 3540. (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 1909 . 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 36302 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1533  wcel 2098
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774  df-nf 1778  df-clel 2804
This theorem is referenced by: (None)
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