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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1373 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj60 29943. 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 |
---|---|
bnj1373.1 |
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bnj1373.2 |
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bnj1373.3 |
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bnj1373.4 |
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bnj1373.5 |
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Ref | Expression |
---|---|
bnj1373 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1373.5 |
. 2
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2 | vex 3034 |
. . 3
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3 | bnj1373.3 |
. . . . . . 7
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4 | bnj1373.1 |
. . . . . . . 8
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5 | 4 | bnj1309 29903 |
. . . . . . 7
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6 | 3, 5 | bnj1307 29904 |
. . . . . 6
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7 | 6 | bnj1351 29710 |
. . . . 5
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8 | 7 | nfi 1682 |
. . . 4
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9 | bnj1373.4 |
. . . . 5
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10 | sneq 3969 |
. . . . . . . 8
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11 | bnj1318 29906 |
. . . . . . . 8
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12 | 10, 11 | uneq12d 3580 |
. . . . . . 7
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13 | 12 | eqeq2d 2481 |
. . . . . 6
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14 | 13 | anbi2d 718 |
. . . . 5
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15 | 9, 14 | syl5bb 265 |
. . . 4
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16 | 8, 15 | sbciegf 3287 |
. . 3
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17 | 2, 16 | ax-mp 5 |
. 2
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18 | 1, 17 | bitri 257 |
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-iun 4271 df-br 4396 df-bnj14 29566 df-bnj18 29572 |
This theorem is referenced by: bnj1374 29912 bnj1384 29913 bnj1398 29915 bnj1450 29931 bnj1489 29937 |
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