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Theorem raleqf 2900
 Description: Equality theorem for restricted universal quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 7-Mar-2004.) (Revised by Andrew Salmon, 11-Jul-2011.)
Hypotheses
Ref Expression
raleq1f.1
raleq1f.2
Assertion
Ref Expression
raleqf

Proof of Theorem raleqf
StepHypRef Expression
1 raleq1f.1 . . . 4
2 raleq1f.2 . . . 4
31, 2nfeq 2579 . . 3
4 eleq2 2497 . . . 4
54imbi1d 309 . . 3
63, 5albid 1788 . 2
7 df-ral 2710 . 2
8 df-ral 2710 . 2
96, 7, 83bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652   wcel 1725  wnfc 2559  wral 2705 This theorem is referenced by:  raleq  2904  raleqbid  23963  dfon2lem3  25412  indexa  26435  stoweidlem28  27753  stoweidlem52  27777 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710
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