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	$$⊢A\in \mathrm{V}$$
	bj-ceqsalv.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	bj-ceqsalv	$$⊢\forall x\left(x=A\to \phi \right)\leftrightarrow \psi$$

Proof

Step	Hyp	Ref	Expression
1		bj-ceqsalv.1	$$⊢A\in \mathrm{V}$$
2		bj-ceqsalv.2	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
3		nfv	$$⊢Ⅎx\psi$$
4	3 1 2	bj-ceqsal	$$⊢\forall x\left(x=A\to \phi \right)\leftrightarrow \psi$$