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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj873 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj69 29891. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj873.4 |
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bnj873.7 |
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bnj873.8 |
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Ref | Expression |
---|---|
bnj873 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj873.4 |
. 2
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2 | nfv 1769 |
. . 3
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3 | nfcv 2612 |
. . . 4
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4 | nfv 1769 |
. . . . 5
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5 | bnj873.7 |
. . . . . 6
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6 | nfsbc1v 3275 |
. . . . . 6
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7 | 5, 6 | nfxfr 1704 |
. . . . 5
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8 | bnj873.8 |
. . . . . 6
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9 | nfsbc1v 3275 |
. . . . . 6
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10 | 8, 9 | nfxfr 1704 |
. . . . 5
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11 | 4, 7, 10 | nf3an 2033 |
. . . 4
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12 | 3, 11 | nfrex 2848 |
. . 3
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13 | fneq1 5674 |
. . . . 5
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14 | sbceq1a 3266 |
. . . . . 6
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15 | 14, 5 | syl6bbr 271 |
. . . . 5
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16 | sbceq1a 3266 |
. . . . . 6
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17 | 16, 8 | syl6bbr 271 |
. . . . 5
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18 | 13, 15, 17 | 3anbi123d 1365 |
. . . 4
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19 | 18 | rexbidv 2892 |
. . 3
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20 | 2, 12, 19 | cbvab 2594 |
. 2
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21 | 1, 20 | eqtri 2493 |
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-or 377 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-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-br 4396 df-opab 4455 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-fun 5591 df-fn 5592 |
This theorem is referenced by: bnj849 29808 bnj893 29811 |
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