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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj919 | Structured version Visualization version Unicode version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj919.1 |
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bnj919.2 |
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bnj919.3 |
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bnj919.4 |
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bnj919.5 |
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Ref | Expression |
---|---|
bnj919 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj919.4 |
. 2
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2 | bnj919.1 |
. . 3
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3 | 2 | sbcbii 3311 |
. 2
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4 | bnj919.5 |
. . 3
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5 | df-bnj17 29564 |
. . . . 5
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6 | nfv 1769 |
. . . . . . 7
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7 | nfv 1769 |
. . . . . . 7
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8 | bnj919.2 |
. . . . . . . 8
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9 | nfsbc1v 3275 |
. . . . . . . 8
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10 | 8, 9 | nfxfr 1704 |
. . . . . . 7
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11 | 6, 7, 10 | nf3an 2033 |
. . . . . 6
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12 | bnj919.3 |
. . . . . . 7
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13 | nfsbc1v 3275 |
. . . . . . 7
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14 | 12, 13 | nfxfr 1704 |
. . . . . 6
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15 | 11, 14 | nfan 2031 |
. . . . 5
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16 | 5, 15 | nfxfr 1704 |
. . . 4
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17 | eleq1 2537 |
. . . . . 6
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18 | fneq2 5675 |
. . . . . . 7
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19 | sbceq1a 3266 |
. . . . . . . 8
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20 | 19, 8 | syl6bbr 271 |
. . . . . . 7
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21 | sbceq1a 3266 |
. . . . . . . 8
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22 | 21, 12 | syl6bbr 271 |
. . . . . . 7
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23 | 18, 20, 22 | 3anbi123d 1365 |
. . . . . 6
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24 | 17, 23 | anbi12d 725 |
. . . . 5
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25 | bnj252 29580 |
. . . . 5
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26 | bnj252 29580 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
27 | 24, 25, 26 | 3bitr4g 296 |
. . . 4
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28 | 16, 27 | sbciegf 3287 |
. . 3
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29 | 4, 28 | ax-mp 5 |
. 2
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30 | 1, 3, 29 | 3bitri 279 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-v 3033 df-sbc 3256 df-fn 5592 df-bnj17 29564 |
This theorem is referenced by: bnj910 29831 bnj999 29840 bnj907 29848 |
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