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Mirrors > Home > MPE Home > Th. List > nfnid | Structured version Visualization version Unicode version |
Description: A setvar variable is not free from itself. The proof relies on dtru 4594, that is, it is not true in a one-element domain. (Contributed by Mario Carneiro, 8-Oct-2016.) |
Ref | Expression |
---|---|
nfnid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dtru 4594 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | ax-ext 2431 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | sps 1943 |
. . . 4
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4 | 3 | alimi 1684 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 1, 4 | mto 180 |
. 2
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6 | df-nfc 2581 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | sbnf2 2268 |
. . . . 5
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8 | elsb4 2264 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | elsb4 2264 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 8, 9 | bibi12i 317 |
. . . . . 6
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11 | 10 | 2albii 1692 |
. . . . 5
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12 | 7, 11 | bitri 253 |
. . . 4
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13 | 12 | albii 1691 |
. . 3
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14 | alrot3 1924 |
. . 3
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15 | 6, 13, 14 | 3bitri 275 |
. 2
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16 | 5, 15 | mtbir 301 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-nul 4534 ax-pow 4581 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-nfc 2581 |
This theorem is referenced by: nfcvb 4630 |
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