Theorem freq1 4854

Description: Equality theorem for the well-founded predicate. (Contributed by NM, 9-Mar-1997.)

Assertion

Ref	Expression
freq1

Proof of Theorem freq1

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

Step	Hyp	Ref	Expression
1		breq 4454	. . . . . 6
2	1	notbid 294	. . . . 5
3	2	rexralbidv 2976	. . . 4
4	3	imbi2d 316	. . 3
5	4	albidv 1713	. 2
6		df-fr 4843	. 2
7		df-fr 4843	. 2
8	5, 6, 7	3bitr4g 288	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  =/=wne 2652  A.wral 2807  E.wrex 2808  C_wss 3475  c0 3784   class class class wbr 4452  Frwfr 4840

This theorem is referenced by:  weeq1  4872  freq12d  30984

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-an 371  df-ex 1613  df-cleq 2449  df-clel 2452  df-ral 2812  df-rex 2813  df-br 4453  df-fr 4843