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Mirrors > Home > ILE Home > Th. List > disjeq2dv | Unicode version |
Description: Equality deduction for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
disjeq2dv.1 |
Ref | Expression |
---|---|
disjeq2dv | Disj Disj |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | disjeq2dv.1 | . . 3 | |
2 | 1 | ralrimiva 2392 | . 2 |
3 | disjeq2 3749 | . 2 Disj Disj | |
4 | 2, 3 | syl 14 | 1 Disj Disj |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 wral 2306 Disj wdisj 3745 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-ral 2311 df-rmo 2314 df-in 2924 df-ss 2931 df-disj 3746 |
This theorem is referenced by: disjeq12d 3754 |
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