Theorem fveqeq2d

Description: Equality deduction for function value. (Contributed by BJ, 30-Aug-2022)

	Ref	Expression
Hypothesis	fveqeq2d.1	$$⊢\phi \to A=B$$
Assertion	fveqeq2d	$$⊢\phi \to \left(F\left(A\right)=C\leftrightarrow F\left(B\right)=C\right)$$

Proof

Step	Hyp	Ref	Expression
1		fveqeq2d.1	$$⊢\phi \to A=B$$
2	1	fveq2d	$$⊢\phi \to F\left(A\right)=F\left(B\right)$$
3	2	eqeq1d	$$⊢\phi \to \left(F\left(A\right)=C\leftrightarrow F\left(B\right)=C\right)$$