Theorem freq12d

Description: Equality deduction for founded relations. (Contributed by Stefan O'Rear, 19-Jan-2015)

	Ref	Expression
Hypotheses	weeq12d.l	|- ( ph -> R = S )
	weeq12d.r	|- ( ph -> A = B )
Assertion	freq12d	|- ( ph -> ( R Fr A <-> S Fr B ) )

Proof

Step	Hyp	Ref	Expression
1		weeq12d.l	|- ( ph -> R = S )
2		weeq12d.r	|- ( ph -> A = B )
3		freq1	|- ( R = S -> ( R Fr A <-> S Fr A ) )
4	1 3	syl	|- ( ph -> ( R Fr A <-> S Fr A ) )
5		freq2	|- ( A = B -> ( S Fr A <-> S Fr B ) )
6	2 5	syl	|- ( ph -> ( S Fr A <-> S Fr B ) )
7	4 6	bitrd	|- ( ph -> ( R Fr A <-> S Fr B ) )