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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 3524 | . . . 4 | |
2 | fvres 5413 | . . . 4 | |
3 | 1, 2 | syl 14 | . . 3 |
4 | resundir 4803 | . . . . 5 | |
5 | elsni 3515 | . . . . . . . . 9 | |
6 | 5 | necon3ai 2334 | . . . . . . . 8 |
7 | ressnop0 5569 | . . . . . . . 8 | |
8 | 6, 7 | syl 14 | . . . . . . 7 |
9 | 8 | uneq2d 3200 | . . . . . 6 |
10 | un0 3366 | . . . . . 6 | |
11 | 9, 10 | syl6eq 2166 | . . . . 5 |
12 | 4, 11 | syl5eq 2162 | . . . 4 |
13 | 12 | fveq1d 5391 | . . 3 |
14 | 3, 13 | sylan9req 2171 | . 2 |
15 | fvres 5413 | . . . 4 | |
16 | 1, 15 | syl 14 | . . 3 |
17 | 16 | adantr 274 | . 2 |
18 | 14, 17 | eqtrd 2150 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1316 wcel 1465 wne 2285 cun 3039 c0 3333 csn 3497 cop 3500 cres 4511 cfv 5093 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-res 4521 df-iota 5058 df-fv 5101 |
This theorem is referenced by: fvpr1 5592 fvpr1g 5594 fvpr2g 5595 fvtp1g 5596 tfrlemisucaccv 6190 tfr1onlemsucaccv 6206 tfrcllemsucaccv 6219 ac6sfi 6760 0tonninf 10180 1tonninf 10181 hashennn 10494 zfz1isolemiso 10550 |
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