Theorem weeq12d

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

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

Proof

Step	Hyp	Ref	Expression
1		weeq12d.l	|- ( ph -> R = S )
2		weeq12d.r	|- ( ph -> A = B )
3		weeq1	|- ( R = S -> ( R We A <-> S We A ) )
4	1 3	syl	|- ( ph -> ( R We A <-> S We A ) )
5		weeq2	|- ( A = B -> ( S We A <-> S We B ) )
6	2 5	syl	|- ( ph -> ( S We A <-> S We B ) )
7	4 6	bitrd	|- ( ph -> ( R We A <-> S We B ) )