Theorem afv2eq1

Description: Equality theorem for function value, analogous to fveq1 . (Contributed by AV, 4-Sep-2022)

	Ref	Expression
Assertion	afv2eq1	$$⊢F=G\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)=\left(G\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢F=G\to F=G$$
2		eqidd	$$⊢F=G\to A=A$$
3	1 2	afv2eq12d	$$⊢F=G\to \left(F\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)=\left(G\mathrm{\text{'}\text{'}\text{'}\text{'}}A\right)$$