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Metamath Proof Explorer

Theorem fveq2

Description: Equality theorem for function value. (Contributed by NM, 29-Dec-1996)

		Ref	Expression
	Assertion	fveq2	$⊢ A = B \to F (A) = F (B)$

Step	Hyp	Ref	Expression
1		breq1	$⊢ A = B \to (A F x \leftrightarrow B F x)$
2	1	iotabidv	$⊢ A = B \to (ι x \| A F x) = (ι x \| B F x)$
3		df-fv	$⊢ F (A) = (ι x \| A F x)$
4		df-fv	$⊢ F (B) = (ι x \| B F x)$
5	2 3 4	3eqtr4g	$⊢ A = B \to F (A) = F (B)$