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Mirrors > Home > ILE Home > Th. List > funssxp | Unicode version |
Description: Two ways of specifying a
partial function from ![]() ![]() |
Ref | Expression |
---|---|
funssxp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn 5261 |
. . . . . 6
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2 | 1 | biimpi 120 |
. . . . 5
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3 | rnss 4872 |
. . . . . 6
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4 | rnxpss 5075 |
. . . . . 6
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5 | 3, 4 | sstrdi 3182 |
. . . . 5
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6 | 2, 5 | anim12i 338 |
. . . 4
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7 | df-f 5235 |
. . . 4
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8 | 6, 7 | sylibr 134 |
. . 3
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9 | dmss 4841 |
. . . . 5
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10 | dmxpss 5074 |
. . . . 5
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11 | 9, 10 | sstrdi 3182 |
. . . 4
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12 | 11 | adantl 277 |
. . 3
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13 | 8, 12 | jca 306 |
. 2
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14 | ffun 5383 |
. . . 4
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15 | 14 | adantr 276 |
. . 3
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16 | fssxp 5398 |
. . . 4
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17 | xpss1 4751 |
. . . 4
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18 | 16, 17 | sylan9ss 3183 |
. . 3
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19 | 15, 18 | jca 306 |
. 2
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20 | 13, 19 | impbii 126 |
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-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-opab 4080 df-xp 4647 df-rel 4648 df-cnv 4649 df-dm 4651 df-rn 4652 df-fun 5233 df-fn 5234 df-f 5235 |
This theorem is referenced by: elpm2g 6683 casef 7105 |
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