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Mirrors > Home > ILE Home > Th. List > fvunsng | Unicode version |
Description: Remove an ordered pair not participating in a function value. (Contributed by Jim Kingdon, 7-Jan-2019.) |
Ref | Expression |
---|---|
fvunsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 3400 | . . . 4 | |
2 | fvres 5198 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | resundir 4626 | . . . . 5 | |
5 | elsni 3393 | . . . . . . . . 9 | |
6 | 5 | necon3ai 2254 | . . . . . . . 8 |
7 | ressnop0 5344 | . . . . . . . 8 | |
8 | 6, 7 | syl 14 | . . . . . . 7 |
9 | 8 | uneq2d 3097 | . . . . . 6 |
10 | un0 3251 | . . . . . 6 | |
11 | 9, 10 | syl6eq 2088 | . . . . 5 |
12 | 4, 11 | syl5eq 2084 | . . . 4 |
13 | 12 | fveq1d 5180 | . . 3 |
14 | 3, 13 | sylan9req 2093 | . 2 |
15 | fvres 5198 | . . . 4 | |
16 | 1, 15 | syl 14 | . . 3 |
17 | 16 | adantr 261 | . 2 |
18 | 14, 17 | eqtrd 2072 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wceq 1243 wcel 1393 wne 2204 cun 2915 c0 3224 csn 3375 cop 3378 cres 4347 cfv 4902 |
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-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 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-uni 3581 df-br 3765 df-opab 3819 df-xp 4351 df-res 4357 df-iota 4867 df-fv 4910 |
This theorem is referenced by: fvpr1 5365 fvpr1g 5367 fvpr2g 5368 fvtp1g 5369 tfrlemisucaccv 5939 ac6sfi 6352 |
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