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Mirrors > Home > NFE Home > Th. List > imakexg | Unicode version |
Description: The image of a set under a set is a set. (Contributed by SF, 14-Jan-2015.) |
Ref | Expression |
---|---|
imakexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfimak2 4299 |
. 2
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2 | 1cex 4143 |
. . . . . 6
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3 | vvex 4110 |
. . . . . 6
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4 | 2, 3 | xpkex 4290 |
. . . . 5
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5 | 4 | complex 4105 |
. . . 4
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6 | xpkexg 4289 |
. . . . . . 7
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7 | 3, 6 | mpan2 652 |
. . . . . 6
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8 | inexg 4101 |
. . . . . 6
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9 | 7, 8 | sylan2 460 |
. . . . 5
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10 | complexg 4100 |
. . . . 5
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11 | sikexg 4297 |
. . . . 5
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12 | 9, 10, 11 | 3syl 18 |
. . . 4
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13 | unexg 4102 |
. . . 4
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14 | 5, 12, 13 | sylancr 644 |
. . 3
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15 | p6exg 4291 |
. . 3
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16 | complexg 4100 |
. . 3
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17 | 14, 15, 16 | 3syl 18 |
. 2
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18 | 1, 17 | syl5eqel 2437 |
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 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 4079 ax-xp 4080 ax-cnv 4081 ax-1c 4082 ax-si 4084 ax-typlower 4087 ax-sn 4088 |
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 2479 df-ne 2519 df-ral 2620 df-rex 2621 df-v 2862 df-nin 3212 df-compl 3213 df-in 3214 df-un 3215 df-dif 3216 df-ss 3260 df-nul 3552 df-sn 3742 df-pr 3743 df-opk 4059 df-1c 4137 df-xpk 4186 df-cnvk 4187 df-imak 4190 df-p6 4192 df-sik 4193 |
This theorem is referenced by: imakex 4301 pw1exg 4303 cokexg 4310 imagekexg 4312 uniexg 4317 intexg 4320 pwexg 4329 addcexg 4394 phiexg 4572 opexg 4588 proj1exg 4592 proj2exg 4593 imaexg 4747 coexg 4750 siexg 4753 |
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