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Theorem nllyeq 17536
 Description: Equality theorem for the Locally predicate. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
nllyeq 𝑛Locally 𝑛Locally

Proof of Theorem nllyeq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2499 . . . . 5 t t
21rexbidv 2728 . . . 4 t t
322ralbidv 2749 . . 3 t t
43rabbidv 2950 . 2 t t
5 df-nlly 17532 . 2 𝑛Locally t
6 df-nlly 17532 . 2 𝑛Locally t
74, 5, 63eqtr4g 2495 1 𝑛Locally 𝑛Locally
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  wral 2707  wrex 2708  crab 2711   cin 3321  cpw 3801  csn 3816  cfv 5456  (class class class)co 6083   ↾t crest 13650  ctop 16960  cnei 17163  𝑛Locally cnlly 17530 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-ral 2712  df-rex 2713  df-rab 2716  df-nlly 17532
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