Theorem bj-ceqsalv

Description: Remove from ceqsalv dependency on ax-ext (and on df-cleq , df-v , df-clab , df-sb ). (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-ceqsalv.1	⊢ 𝐴 ∈ V
	bj-ceqsalv.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
Assertion	bj-ceqsalv	⊢ ( ∀ 𝑥 ( 𝑥 = 𝐴 → 𝜑 ) ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		bj-ceqsalv.1	⊢ 𝐴 ∈ V
2		bj-ceqsalv.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	3 1 2	bj-ceqsal	⊢ ( ∀ 𝑥 ( 𝑥 = 𝐴 → 𝜑 ) ↔ 𝜓 )