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Theorem llyeq 20416
 Description: Equality theorem for the Locally predicate. (Contributed by Mario Carneiro, 2-Mar-2015.)
Assertion
Ref Expression
llyeq Locally Locally

Proof of Theorem llyeq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2502 . . . . . 6 t t
21anbi2d 708 . . . . 5 t t
32rexbidv 2946 . . . 4 t t
432ralbidv 2876 . . 3 t t
54rabbidv 3079 . 2 t t
6 df-lly 20412 . 2 Locally t
7 df-lly 20412 . 2 Locally t
85, 6, 73eqtr4g 2495 1 Locally Locally
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1870  wral 2782  wrex 2783  crab 2786   cin 3441  cpw 3985  (class class class)co 6305   ↾t crest 15278  ctop 19848  Locally clly 20410 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-ral 2787  df-rex 2788  df-rab 2791  df-lly 20412 This theorem is referenced by:  ismntoplly  28668
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