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Theorem disjeq1 4192
 Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjeq1 Disj Disj
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem disjeq1
StepHypRef Expression
1 eqimss2 3403 . . 3
2 disjss1 4191 . . 3 Disj Disj
31, 2syl 16 . 2 Disj Disj
4 eqimss 3402 . . 3
5 disjss1 4191 . . 3 Disj Disj
64, 5syl 16 . 2 Disj Disj
73, 6impbid 185 1 Disj Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653   wss 3322  Disj wdisj 4185 This theorem is referenced by:  disjeq1d  4193  volfiniun  19446  iundisj2cnt  24160  measvun  24568 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-rmo 2715  df-in 3329  df-ss 3336  df-disj 4186
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