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Mirrors > Home > ILE Home > Th. List > Mathboxes > elabgft1 | Unicode version |
Description: One implication of elabgf 2902, in closed form. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
elabgf1.nf1 |
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elabgf1.nf2 |
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Ref | Expression |
---|---|
elabgft1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimp 118 |
. . . . . 6
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2 | imim2 55 |
. . . . . 6
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3 | 1, 2 | syl5 32 |
. . . . 5
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4 | 3 | imim2i 12 |
. . . 4
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5 | 4 | alimi 1466 |
. . 3
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6 | elabgf1.nf1 |
. . . 4
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7 | nfab1 2338 |
. . . . . 6
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8 | 6, 7 | nfel 2345 |
. . . . 5
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9 | elabgf1.nf2 |
. . . . 5
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10 | 8, 9 | nfim 1583 |
. . . 4
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11 | elabgf0 15214 |
. . . 4
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12 | 6, 10, 11 | bj-vtoclgft 15212 |
. . 3
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13 | 5, 12 | syl 14 |
. 2
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14 | 13 | pm2.43d 50 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 |
This theorem is referenced by: elabgf1 15216 |
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