Theorem bj-vtocl 37579

Description: Remove dependency on ax-ext 2734, df-clab 2741 and df-cleq 2754 (and df-sb 2096 and df-v 3456) from vtocl 3524. (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 1943	. 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 37578	1 ⊢ 𝜓

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   = wceq 1569   ∈ wcel 2142

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-8 2144  ax-12 2212

This proof depends on definitions:  df-bi 210  df-an 401  df-ex 1809  df-nf 1813  df-clel 2837

This theorem is used by: (None)