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Mirrors > Home > NFE Home > Th. List > 2ralunsn | Unicode version |
Description: Double restricted quantification over the union of a set and a singleton, using implicit substitution. (Contributed by Paul Chapman, 17-Nov-2012.) |
Ref | Expression |
---|---|
2ralunsn.1 |
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2ralunsn.2 |
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2ralunsn.3 |
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Ref | Expression |
---|---|
2ralunsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2ralunsn.2 |
. . . 4
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2 | 1 | ralunsn 3879 |
. . 3
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3 | 2 | ralbidv 2634 |
. 2
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4 | 2ralunsn.1 |
. . . . . 6
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5 | 4 | ralbidv 2634 |
. . . . 5
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6 | 2ralunsn.3 |
. . . . 5
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7 | 5, 6 | anbi12d 691 |
. . . 4
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8 | 7 | ralunsn 3879 |
. . 3
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9 | r19.26 2746 |
. . . 4
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10 | 9 | anbi1i 676 |
. . 3
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11 | 8, 10 | syl6bb 252 |
. 2
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12 | 3, 11 | bitrd 244 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 |
This theorem is referenced by: (None) |
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