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Theorem raleqf 2803
 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 2496 . . 3
4 eleq2 2414 . . . 4
54imbi1d 308 . . 3
63, 5albid 1772 . 2
7 df-ral 2619 . 2
8 df-ral 2619 . 2
96, 7, 83bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710  wnfc 2476  wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619 This theorem is referenced by:  raleq  2807
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