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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nuliota | Structured version Visualization version Unicode version |
Description: Definition of the empty set using the definite description binder. See also bj-nuliotaALT 31626. (Contributed by BJ, 30-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nuliota |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 4507 |
. . . 4
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2 | 1 | eueq1 3179 |
. . . . 5
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3 | eq0 3715 |
. . . . . 6
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4 | 3 | eubii 2322 |
. . . . 5
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5 | 2, 4 | mpbi 213 |
. . . 4
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6 | eleq2 2519 |
. . . . . . 7
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7 | 6 | notbid 300 |
. . . . . 6
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8 | 7 | albidv 1771 |
. . . . 5
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9 | 8 | iota2 5551 |
. . . 4
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10 | 1, 5, 9 | mp2an 683 |
. . 3
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11 | noel 3703 |
. . 3
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12 | 10, 11 | mpgbi 1676 |
. 2
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13 | 12 | eqcomi 2461 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-nul 4506 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-ral 2742 df-rex 2743 df-v 3015 df-sbc 3236 df-dif 3375 df-un 3377 df-nul 3700 df-sn 3937 df-pr 3939 df-uni 4169 df-iota 5525 |
This theorem is referenced by: (None) |
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