Theorem eccnvepex

Description: The converse epsilon coset exists. (Contributed by Peter Mazsa, 22-Mar-2023)

	Ref	Expression
Assertion	eccnvepex	⊢ [ 𝐴 ] ◡ E ∈ V

Proof

Step	Hyp	Ref	Expression
1		snex	⊢ { 𝐴 } ∈ V
2		cnvepresex	⊢ ( { 𝐴 } ∈ V → ( ◡ E ↾ { 𝐴 } ) ∈ V )
3		ecexALTV	⊢ ( ( ◡ E ↾ { 𝐴 } ) ∈ V → [ 𝐴 ] ◡ E ∈ V )
4	1 2 3	mp2b	⊢ [ 𝐴 ] ◡ E ∈ V