Theorem symgfv

Description: The function value of a permutation. (Contributed by AV, 1-Jan-2019)

	Ref	Expression
Hypotheses	symgbas.1	|- G = ( SymGrp ` A )
	symgbas.2	|- B = ( Base ` G )
Assertion	symgfv	|- ( ( F e. B /\ X e. A ) -> ( F ` X ) e. A )

Proof

Step	Hyp	Ref	Expression
1		symgbas.1	|- G = ( SymGrp ` A )
2		symgbas.2	|- B = ( Base ` G )
3	1 2	symgbasf	|- ( F e. B -> F : A --> A )
4	3	ffvelcdmda	|- ( ( F e. B /\ X e. A ) -> ( F ` X ) e. A )