Theorem cleqfOLD 2647

Description: Obsolete proof of cleqf 2646 as of 17-Nov-2019. (Contributed by NM, 26-May-1993.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
cleqf.1
cleqf.2

Assertion

Ref	Expression
cleqfOLD

Proof of Theorem cleqfOLD

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		dfcleq 2450	. 2
2		nfv 1707	. . 3
3		cleqf.1	. . . . 5
4	3	nfcri 2612	. . . 4
5		cleqf.2	. . . . 5
6	5	nfcri 2612	. . . 4
7	4, 6	nfbi 1934	. . 3
8		eleq1 2529	. . . 4
9		eleq1 2529	. . . 4
10	8, 9	bibi12d 321	. . 3
11	2, 7, 10	cbval 2021	. 2
12	1, 11	bitr4i 252	1

Syntax hints:  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  F/_wnfc 2605

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-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607