Theorem seeq12d

Description: Equality deduction for the set-like predicate. (Contributed by Matthew House, 10-Sep-2025)

	Ref	Expression
Hypotheses	seeq12d.1	|- ( ph -> R = S )
	seeq12d.2	|- ( ph -> A = B )
Assertion	seeq12d	|- ( ph -> ( R Se A <-> S Se B ) )

Proof

Step	Hyp	Ref	Expression
1		seeq12d.1	|- ( ph -> R = S )
2		seeq12d.2	|- ( ph -> A = B )
3		seeq1	|- ( R = S -> ( R Se A <-> S Se A ) )
4		seeq2	|- ( A = B -> ( S Se A <-> S Se B ) )
5	3 4	sylan9bb	|- ( ( R = S /\ A = B ) -> ( R Se A <-> S Se B ) )
6	1 2 5	syl2anc	|- ( ph -> ( R Se A <-> S Se B ) )