Theorem soeq1 4824

Description: Equality theorem for the strict ordering predicate. (Contributed by NM, 16-Mar-1997.)

Assertion

Ref	Expression
soeq1

Proof of Theorem soeq1

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		poeq1 4808	. . 3
2		breq 4454	. . . . 5
3		biidd 237	. . . . 5
4		breq 4454	. . . . 5
5	2, 3, 4	3orbi123d 1298	. . . 4
6	5	2ralbidv 2901	. . 3
7	1, 6	anbi12d 710	. 2
8		df-so 4806	. 2
9		df-so 4806	. 2
10	7, 8, 9	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  \/w3o 972  =wceq 1395  A.wral 2807   class class class wbr 4452  Powpo 4803  Orwor 4804

This theorem is referenced by:  weeq1  4872  ltsopi  9287  cnso  13980  opsrtoslem2  18149  soeq12d  30983

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-ex 1613  df-cleq 2449  df-clel 2452  df-ral 2812  df-br 4453  df-po 4805  df-so 4806