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Mirrors > Home > ILE Home > Th. List > disjeq1 | Unicode version |
Description: Equality theorem for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
disjeq1 | Disj Disj |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3152 | . . 3 | |
2 | disjss1 3912 | . . 3 Disj Disj | |
3 | 1, 2 | syl 14 | . 2 Disj Disj |
4 | eqimss 3151 | . . 3 | |
5 | disjss1 3912 | . . 3 Disj Disj | |
6 | 4, 5 | syl 14 | . 2 Disj Disj |
7 | 3, 6 | impbid 128 | 1 Disj Disj |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 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-rmo 2424 df-in 3077 df-ss 3084 df-disj 3907 |
This theorem is referenced by: disjeq1d 3914 |
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