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

Theorem rexeqf 3051
Description: Equality theorem for restricted existential quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 9-Oct-2003.) (Revised by Andrew Salmon, 11-Jul-2011.)
Hypotheses
Ref Expression
raleq1f.1
raleq1f.2
Assertion
Ref Expression
rexeqf

Proof of Theorem rexeqf
StepHypRef Expression
1 raleq1f.1 . . . 4
2 raleq1f.2 . . . 4
31, 2nfeq 2630 . . 3
4 eleq2 2530 . . . 4
54anbi1d 704 . . 3
63, 5exbid 1886 . 2
7 df-rex 2813 . 2
8 df-rex 2813 . 2
96, 7, 83bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  F/_wnfc 2605  E.wrex 2808
This theorem is referenced by:  rexeq  3055  rexeqbid  3067  zfrep6  6768  iuneq12daf  27425  indexa  30224
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-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813
  Copyright terms: Public domain W3C validator