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Mirrors > Home > MPE Home > Th. List > disjeq2dv | Structured version Visualization version Unicode version |
Description: Equality deduction for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
disjeq2dv.1 |
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Ref | Expression |
---|---|
disjeq2dv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | disjeq2dv.1 |
. . 3
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2 | 1 | ralrimiva 2813 |
. 2
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3 | disjeq2 4390 |
. 2
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4 | 2, 3 | syl 17 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-ral 2753 df-rmo 2756 df-in 3422 df-ss 3429 df-disj 4387 |
This theorem is referenced by: disjeq12d 4395 iunmbl 22554 uniioovol 22584 carsggect 29198 voliunnfl 32028 nnfoctbdjlem 38330 meadjiun 38341 |
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