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Mirrors > Home > ILE Home > Th. List > tfrlemibacc | Unicode version |
Description: Each element of is an acceptable function. Lemma for tfrlemi1 6279. (Contributed by Jim Kingdon, 14-Mar-2019.) (Proof shortened by Mario Carneiro, 24-May-2019.) |
Ref | Expression |
---|---|
tfrlemisucfn.1 | |
tfrlemisucfn.2 | |
tfrlemi1.3 | |
tfrlemi1.4 | |
tfrlemi1.5 |
Ref | Expression |
---|---|
tfrlemibacc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlemi1.3 | . 2 | |
2 | simpr3 990 | . . . . . . 7 | |
3 | tfrlemisucfn.1 | . . . . . . . 8 | |
4 | tfrlemisucfn.2 | . . . . . . . . 9 | |
5 | 4 | ad2antrr 480 | . . . . . . . 8 |
6 | tfrlemi1.4 | . . . . . . . . . 10 | |
7 | 6 | ad2antrr 480 | . . . . . . . . 9 |
8 | simplr 520 | . . . . . . . . 9 | |
9 | onelon 4344 | . . . . . . . . 9 | |
10 | 7, 8, 9 | syl2anc 409 | . . . . . . . 8 |
11 | simpr1 988 | . . . . . . . 8 | |
12 | simpr2 989 | . . . . . . . 8 | |
13 | 3, 5, 10, 11, 12 | tfrlemisucaccv 6272 | . . . . . . 7 |
14 | 2, 13 | eqeltrd 2234 | . . . . . 6 |
15 | 14 | ex 114 | . . . . 5 |
16 | 15 | exlimdv 1799 | . . . 4 |
17 | 16 | rexlimdva 2574 | . . 3 |
18 | 17 | abssdv 3202 | . 2 |
19 | 1, 18 | eqsstrid 3174 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wal 1333 wceq 1335 wex 1472 wcel 2128 cab 2143 wral 2435 wrex 2436 cvv 2712 cun 3100 wss 3102 csn 3560 cop 3563 con0 4323 cres 4588 wfun 5164 wfn 5165 cfv 5170 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-setind 4496 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-tr 4063 df-id 4253 df-iord 4326 df-on 4328 df-suc 4331 df-xp 4592 df-rel 4593 df-cnv 4594 df-co 4595 df-dm 4596 df-res 4598 df-iota 5135 df-fun 5172 df-fn 5173 df-fv 5178 |
This theorem is referenced by: tfrlemibfn 6275 tfrlemiubacc 6277 |
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