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Theorem disjeq2 3910
 Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.)
Assertion
Ref Expression
disjeq2 Disj Disj

Proof of Theorem disjeq2
StepHypRef Expression
1 eqimss2 3152 . . . 4
21ralimi 2495 . . 3
3 disjss2 3909 . . 3 Disj Disj
42, 3syl 14 . 2 Disj Disj
5 eqimss 3151 . . . 4
65ralimi 2495 . . 3
7 disjss2 3909 . . 3 Disj Disj
86, 7syl 14 . 2 Disj Disj
94, 8impbid 128 1 Disj Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1331  wral 2416   wss 3071  Disj wdisj 3906 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-ral 2421  df-rmo 2424  df-in 3077  df-ss 3084  df-disj 3907 This theorem is referenced by:  disjeq2dv  3911
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