Theorem cleqhOLD 2573

Description: Obsolete proof of cleqh 2572 as of 14-Nov-2019. (Contributed by NM, 26-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
cleqh.1
cleqh.2

Assertion

Ref	Expression
cleqhOLD

Distinct variable groups:   ,   ,   ,

Proof of Theorem cleqhOLD

Step	Hyp	Ref	Expression
1		dfcleq 2450	. 2
2		ax-5 1704	. . . 4
3		dfbi2 628	. . . . 5
4		cleqh.1	. . . . . . 7
5		cleqh.2	. . . . . . 7
6	4, 5	hbim 1922	. . . . . 6
7	5, 4	hbim 1922	. . . . . 6
8	6, 7	hban 1931	. . . . 5
9	3, 8	hbxfrbi 1643	. . . 4
10		eleq1 2529	. . . . . 6
11		eleq1 2529	. . . . . 6
12	10, 11	bibi12d 321	. . . . 5
13	12	biimpd 207	. . . 4
14	2, 9, 13	cbv3h 2016	. . 3
15	12	equcoms 1795	. . . . 5
16	15	biimprd 223	. . . 4
17	9, 2, 16	cbv3h 2016	. . 3
18	14, 17	impbii 188	. 2
19	1, 18	bitr4i 252	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818

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-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452