Theorem soeq12d

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

	Ref	Expression
Hypotheses	weeq12d.l	|- ( ph -> R = S )
	weeq12d.r	|- ( ph -> A = B )
Assertion	soeq12d	|- ( ph -> ( R Or A <-> S Or B ) )

Proof

Step	Hyp	Ref	Expression
1		weeq12d.l	|- ( ph -> R = S )
2		weeq12d.r	|- ( ph -> A = B )
3		soeq1	|- ( R = S -> ( R Or A <-> S Or A ) )
4	1 3	syl	|- ( ph -> ( R Or A <-> S Or A ) )
5		soeq2	|- ( A = B -> ( S Or A <-> S Or B ) )
6	2 5	syl	|- ( ph -> ( S Or A <-> S Or B ) )
7	4 6	bitrd	|- ( ph -> ( R Or A <-> S Or B ) )