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Mirrors > Home > ILE Home > Th. List > tfrlemisucfn | Unicode version |
Description: We can extend an acceptable function by one element to produce a function. Lemma for tfrlemi1 5946. (Contributed by Jim Kingdon, 2-Jul-2019.) |
Ref | Expression |
---|---|
tfrlemisucfn.1 | |
tfrlemisucfn.2 | |
tfrlemisucfn.3 | |
tfrlemisucfn.4 | |
tfrlemisucfn.5 |
Ref | Expression |
---|---|
tfrlemisucfn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2560 | . . 3 | |
2 | 1 | a1i 9 | . 2 |
3 | tfrlemisucfn.2 | . . . 4 | |
4 | 3 | tfrlem3-2d 5928 | . . 3 |
5 | 4 | simprd 107 | . 2 |
6 | tfrlemisucfn.4 | . 2 | |
7 | eqid 2040 | . 2 | |
8 | df-suc 4108 | . 2 | |
9 | elirrv 4272 | . . 3 | |
10 | 9 | a1i 9 | . 2 |
11 | 2, 5, 6, 7, 8, 10 | fnunsn 5006 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wal 1241 wceq 1243 wcel 1393 cab 2026 wral 2306 wrex 2307 cvv 2557 cun 2915 csn 3375 cop 3378 con0 4100 csuc 4102 cres 4347 wfun 4896 wfn 4897 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 ax-setind 4262 |
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-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-id 4030 df-suc 4108 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fn 4905 df-fv 4910 |
This theorem is referenced by: tfrlemisucaccv 5939 tfrlemibfn 5942 |
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