Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  disjeq1d Unicode version

Theorem disjeq1d 4430
 Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypothesis
Ref Expression
disjeq1d.1
Assertion
Ref Expression
disjeq1d
Distinct variable groups:   ,   ,

Proof of Theorem disjeq1d
StepHypRef Expression
1 disjeq1d.1 . 2
2 disjeq1 4429 . 2
31, 2syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  Disj_wdisj 4422 This theorem is referenced by:  disjeq12d  4431  disjxiun  4449  disjdifprg  27436  disjdifprg2  27437  measxun2  28181  measssd  28186 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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-rmo 2815  df-in 3482  df-ss 3489  df-disj 4423
 Copyright terms: Public domain W3C validator