Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  raleqf Structured version   Visualization version   Unicode version

Theorem raleqf 2969
 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 2623 . . 3
4 eleq2 2538 . . . 4
54imbi1d 324 . . 3
63, 5albid 1983 . 2
7 df-ral 2761 . 2
8 df-ral 2761 . 2
96, 7, 83bitr4g 296 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450   wceq 1452   wcel 1904  wnfc 2599  wral 2756 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761 This theorem is referenced by:  raleq  2973  raleqbid  2985  dfon2lem3  30502  indexa  32124  ralbi12f  32468  iineq12f  32472  ac6s6f  32480  stoweidlem28  38000  stoweidlem52  38025  fourierdlem31  38112  fourierdlem31OLD  38113  fourierdlem68  38150  fourierdlem103  38185  fourierdlem104  38186
 Copyright terms: Public domain W3C validator