Mathbox for Drahflow < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcung Structured version   Unicode version

Theorem sbcung 25117
 Description: Distribution of class substitution over union of two classes. (Contributed by Drahflow, 23-Sep-2015.) (Revised by Mario Carneiro, 11-Dec-2016.)
Assertion
Ref Expression
sbcung
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcung
StepHypRef Expression
1 nfcsb1v 3276 . . . 4
2 nfcsb1v 3276 . . . 4
31, 2nfun 3496 . . 3
43a1i 11 . 2
5 csbeq1a 3252 . . 3
6 csbeq1a 3252 . . 3
75, 6uneq12d 3495 . 2
84, 7csbiegf 3284 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wnfc 2559  cvv 2949  csb 3244   cun 3311 This theorem is referenced by:  sbcuni  25118 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2951  df-sbc 3155  df-csb 3245  df-un 3318
 Copyright terms: Public domain W3C validator