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Mirrors > Home > MPE Home > Th. List > notzfaus | Structured version Visualization version Unicode version |
Description: In the Separation Scheme
zfauscl 4526, we require that ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
notzfaus.1 |
![]() ![]() ![]() ![]() ![]() ![]() |
notzfaus.2 |
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Ref | Expression |
---|---|
notzfaus |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | notzfaus.1 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 0ex 4534 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
3 | 2 | snnz 4089 |
. . . . . 6
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4 | 1, 3 | eqnetri 2693 |
. . . . 5
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5 | n0 3740 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 4, 5 | mpbi 212 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() |
7 | biimt 337 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | iman 426 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | notzfaus.2 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9 | anbi2i 699 |
. . . . . . 7
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11 | 8, 10 | xchbinxr 313 |
. . . . . 6
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12 | 7, 11 | syl6bb 265 |
. . . . 5
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13 | xor3 359 |
. . . . 5
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14 | 12, 13 | sylibr 216 |
. . . 4
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15 | 6, 14 | eximii 1708 |
. . 3
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16 | exnal 1698 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 15, 16 | mpbi 212 |
. 2
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18 | 17 | nex 1677 |
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-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-nul 4533 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-v 3046 df-dif 3406 df-nul 3731 df-sn 3968 |
This theorem is referenced by: (None) |
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