Theorem bj-vtocl 36895

Description: Remove dependency on ax-ext 2707, df-clab 2714 and df-cleq 2728 (and df-sb 2065 and df-v 3481) from vtocl 3557. (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 1914	. 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 36894	1 ⊢ 𝜓

Syntax hints:   → wi 4   ↔ wb 206   = wceq 1540   ∈ wcel 2108

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-12 2177

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-nf 1784  df-clel 2815

This theorem is referenced by: (None)