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Theorem bj-vtocl 32101
 Description: Remove dependency on ax-ext 2590, df-clab 2597 and df-cleq 2603 (and df-sb 1868 and df-v 3175) from vtocl 3232. (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 1830 . 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 32100 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   = wceq 1475   ∈ wcel 1977 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701  df-clel 2606 This theorem is referenced by: (None)
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