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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-nfeqfb | Structured version Visualization version Unicode version |
Description: Extend nfeqf 2138 to an equivalence. (Contributed by Wolf Lammen, 31-Jul-2019.) |
Ref | Expression |
---|---|
wl-nfeqfb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfr 1950 |
. . . . 5
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2 | 1 | imp 431 |
. . . 4
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3 | wl-aleq 31861 |
. . . . 5
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4 | 3 | simprbi 466 |
. . . 4
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5 | 2, 4 | syl 17 |
. . 3
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6 | nfnt 1981 |
. . . . . 6
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7 | 6 | nfrd 1952 |
. . . . 5
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8 | 7 | imp 431 |
. . . 4
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9 | alnex 1664 |
. . . . . 6
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10 | wl-exeq 31860 |
. . . . . 6
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11 | 9, 10 | xchbinx 312 |
. . . . 5
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12 | 3ioran 1002 |
. . . . 5
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13 | 11, 12 | sylbb 201 |
. . . 4
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14 | 3simpc 1006 |
. . . 4
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15 | pm5.21 868 |
. . . 4
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16 | 8, 13, 14, 15 | 4syl 19 |
. . 3
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17 | 5, 16 | pm2.61dan 799 |
. 2
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18 | ax7 1859 |
. . . . 5
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19 | 18 | al2imi 1686 |
. . . 4
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20 | wl-nftht 31862 |
. . . 4
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21 | 19, 20 | syl6 34 |
. . 3
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22 | nfeqf 2138 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 22 | ex 436 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 21, 23 | bija 357 |
. 2
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25 | 17, 24 | impbii 191 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-12 1932 ax-13 2090 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 985 df-3an 986 df-ex 1663 df-nf 1667 |
This theorem is referenced by: (None) |
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