Theorem cnvepimaex

Description: The image of converse epsilon exists, proof via imaexALTV (see also cnvepima and uniexg for alternate way). (Contributed by Peter Mazsa, 22-Mar-2023)

	Ref	Expression
Assertion	cnvepimaex	|- ( A e. V -> ( `' _E " A ) e. _V )

Proof

Step	Hyp	Ref	Expression
1		cnvepresex	|- ( A e. V -> ( `' _E |` A ) e. _V )
2		imaexALTV	|- ( ( `' _E e. _V \/ ( ( `' _E |` A ) e. _V /\ A e. V ) ) -> ( `' _E " A ) e. _V )
3	2	olcs	|- ( ( ( `' _E |` A ) e. _V /\ A e. V ) -> ( `' _E " A ) e. _V )
4	1 3	mpancom	|- ( A e. V -> ( `' _E " A ) e. _V )