Theorem fundcmpsurinjlem1

Description: Lemma 1 for fundcmpsurinj . (Contributed by AV, 4-Mar-2024)

	Ref	Expression
Hypotheses	fundcmpsurinj.p	|- P = { z | E. x e. A z = ( `' F " { ( F ` x ) } ) }
	fundcmpsurinj.g	|- G = ( x e. A |-> ( `' F " { ( F ` x ) } ) )
Assertion	fundcmpsurinjlem1	|- ran G = P

Proof

Step	Hyp	Ref	Expression
1		fundcmpsurinj.p	|- P = { z | E. x e. A z = ( `' F " { ( F ` x ) } ) }
2		fundcmpsurinj.g	|- G = ( x e. A |-> ( `' F " { ( F ` x ) } ) )
3	2	rnmpt	|- ran G = { z | E. x e. A z = ( `' F " { ( F ` x ) } ) }
4	3 1	eqtr4i	|- ran G = P