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

Theorem rabeqbidva 3105
Description: Equality of restricted class abstractions. (Contributed by Mario Carneiro, 26-Jan-2017.)
Hypotheses
Ref Expression
rabeqbidva.1
rabeqbidva.2
Assertion
Ref Expression
rabeqbidva
Distinct variable groups:   ,   ,   ,

Proof of Theorem rabeqbidva
StepHypRef Expression
1 rabeqbidva.2 . . 3
21rabbidva 3100 . 2
3 rabeqbidva.1 . . 3
4 rabeq 3103 . . 3
53, 4syl 16 . 2
62, 5eqtrd 2498 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  {crab 2811
This theorem is referenced by:  natpropd  15345  gsumpropd2lem  15900  eengv  24282  elntg  24287  domnmsuppn0  32962
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-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816
  Copyright terms: Public domain W3C validator