Theorem 1cosscnvepresex

Description: Sufficient condition for a restricted converse epsilon coset to be a set. (Contributed by Peter Mazsa, 24-Sep-2021)

	Ref	Expression
Assertion	1cosscnvepresex	$$⊢A\in V\to \wr \left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		cnvepresex	$$⊢A\in V\to {{\mathrm{E}}^{-1}\upharpoonright }_A\in \mathrm{V}$$
2		cossex	$$⊢{{\mathrm{E}}^{-1}\upharpoonright }_A\in \mathrm{V}\to \wr \left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)\in \mathrm{V}$$
3	1 2	syl	$$⊢A\in V\to \wr \left({{\mathrm{E}}^{-1}\upharpoonright }_A\right)\in \mathrm{V}$$