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Mirrors > Home > NFE Home > Th. List > p6exg | Unicode version |
Description: The P6 operator applied to a set yields a set. (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
p6exg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | p6eq 4238 |
. . 3
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2 | 1 | eleq1d 2419 |
. 2
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3 | ax-typlower 4086 |
. . 3
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4 | dfcleq 2347 |
. . . . . . 7
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5 | vex 2862 |
. . . . . . . . . 10
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6 | elp6 4263 |
. . . . . . . . . 10
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7 | 5, 6 | ax-mp 8 |
. . . . . . . . 9
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8 | 7 | bibi2i 304 |
. . . . . . . 8
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9 | 8 | albii 1566 |
. . . . . . 7
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10 | 4, 9 | bitri 240 |
. . . . . 6
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11 | 10 | biimpri 197 |
. . . . 5
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12 | vex 2862 |
. . . . 5
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13 | 11, 12 | syl6eqelr 2442 |
. . . 4
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14 | 13 | exlimiv 1634 |
. . 3
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15 | 3, 14 | ax-mp 8 |
. 2
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16 | 2, 15 | vtoclg 2914 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-pr 3742 df-opk 4058 df-xpk 4185 df-p6 4191 |
This theorem is referenced by: uni1exg 4292 imakexg 4299 |
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