Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > tfr1onlembacc | Unicode version |
Description: Lemma for tfr1on 6215. Each element of is an acceptable function. (Contributed by Jim Kingdon, 14-Mar-2022.) |
Ref | Expression |
---|---|
tfr1on.f | recs |
tfr1on.g | |
tfr1on.x | |
tfr1on.ex | |
tfr1onlemsucfn.1 | |
tfr1onlembacc.3 | |
tfr1onlembacc.u | |
tfr1onlembacc.4 | |
tfr1onlembacc.5 |
Ref | Expression |
---|---|
tfr1onlembacc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfr1onlembacc.3 | . 2 | |
2 | simpr3 974 | . . . . . . 7 | |
3 | tfr1on.f | . . . . . . . 8 recs | |
4 | tfr1on.g | . . . . . . . . 9 | |
5 | 4 | ad2antrr 479 | . . . . . . . 8 |
6 | tfr1on.x | . . . . . . . . 9 | |
7 | 6 | ad2antrr 479 | . . . . . . . 8 |
8 | tfr1on.ex | . . . . . . . . . 10 | |
9 | 8 | 3adant1r 1194 | . . . . . . . . 9 |
10 | 9 | 3adant1r 1194 | . . . . . . . 8 |
11 | tfr1onlemsucfn.1 | . . . . . . . 8 | |
12 | tfr1onlembacc.4 | . . . . . . . . 9 | |
13 | 12 | ad2antrr 479 | . . . . . . . 8 |
14 | simplr 504 | . . . . . . . 8 | |
15 | tfr1onlembacc.u | . . . . . . . . . 10 | |
16 | 15 | adantlr 468 | . . . . . . . . 9 |
17 | 16 | adantlr 468 | . . . . . . . 8 |
18 | simpr1 972 | . . . . . . . 8 | |
19 | simpr2 973 | . . . . . . . 8 | |
20 | 3, 5, 7, 10, 11, 13, 14, 17, 18, 19 | tfr1onlemsucaccv 6206 | . . . . . . 7 |
21 | 2, 20 | eqeltrd 2194 | . . . . . 6 |
22 | 21 | ex 114 | . . . . 5 |
23 | 22 | exlimdv 1775 | . . . 4 |
24 | 23 | rexlimdva 2526 | . . 3 |
25 | 24 | abssdv 3141 | . 2 |
26 | 1, 25 | eqsstrid 3113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wceq 1316 wex 1453 wcel 1465 cab 2103 wral 2393 wrex 2394 cvv 2660 cun 3039 wss 3041 csn 3497 cop 3500 cuni 3706 word 4254 csuc 4257 cres 4511 wfun 5087 wfn 5088 cfv 5093 recscrecs 6169 |
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-13 1476 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 ax-un 4325 ax-setind 4422 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 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-sbc 2883 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-tr 3997 df-id 4185 df-iord 4258 df-on 4260 df-suc 4263 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-res 4521 df-iota 5058 df-fun 5095 df-fn 5096 df-fv 5101 |
This theorem is referenced by: tfr1onlembfn 6209 tfr1onlemubacc 6211 |
Copyright terms: Public domain | W3C validator |