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	⊢ 𝐴 ∈ 𝑉
bj-vtocl.maj	⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓))
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

Step	Hyp	Ref	Expression
1		nfv 1830	. 2 ⊢ Ⅎ𝑥𝜓
2		bj-vtocl.s	. 2 ⊢ 𝐴 ∈ 𝑉
3		bj-vtocl.maj	. 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓))
4		bj-vtocl.min	. 2 ⊢ 𝜑
5	1, 2, 3, 4	bj-vtoclf 32100	1 ⊢ 𝜓

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)