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Theorem freq1 4544
 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.
StepHypRef Expression
1 breq 4206 . . . . . 6
21notbid 286 . . . . 5
32rexralbidv 2741 . . . 4
43imbi2d 308 . . 3
54albidv 1635 . 2
6 df-fr 4533 . 2
7 df-fr 4533 . 2
85, 6, 73bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wne 2598  wral 2697  wrex 2698   wss 3312  c0 3620   class class class wbr 4204   wfr 4530 This theorem is referenced by:  weeq1  4562  freq12d  27067 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-cleq 2428  df-clel 2431  df-ral 2702  df-rex 2703  df-br 4205  df-fr 4533
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