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Mirrors > Home > ILE Home > Th. List > fsnunf | Unicode version |
Description: Adjoining a point to a function gives a function. (Contributed by Stefan O'Rear, 28-Feb-2015.) |
Ref | Expression |
---|---|
fsnunf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 904 | . . 3 | |
2 | simp2l 930 | . . . . 5 | |
3 | simp3 906 | . . . . 5 | |
4 | f1osng 5167 | . . . . 5 | |
5 | 2, 3, 4 | syl2anc 391 | . . . 4 |
6 | f1of 5126 | . . . 4 | |
7 | 5, 6 | syl 14 | . . 3 |
8 | simp2r 931 | . . . 4 | |
9 | disjsn 3432 | . . . 4 | |
10 | 8, 9 | sylibr 137 | . . 3 |
11 | fun 5063 | . . 3 | |
12 | 1, 7, 10, 11 | syl21anc 1134 | . 2 |
13 | snssi 3508 | . . . . 5 | |
14 | 13 | 3ad2ant3 927 | . . . 4 |
15 | ssequn2 3116 | . . . 4 | |
16 | 14, 15 | sylib 127 | . . 3 |
17 | feq3 5032 | . . 3 | |
18 | 16, 17 | syl 14 | . 2 |
19 | 12, 18 | mpbid 135 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 cun 2915 cin 2916 wss 2917 c0 3224 csn 3375 cop 3378 wf 4898 wf1o 4901 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-nul 3225 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 |
This theorem is referenced by: (None) |
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