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Mirrors > Home > ILE Home > Th. List > tfr1onlemssrecs | Unicode version |
Description: Lemma for tfr1on 6215. The union of functions acceptable for tfr1on 6215 is a subset of recs. (Contributed by Jim Kingdon, 15-Mar-2022.) |
Ref | Expression |
---|---|
tfr1onlemssrecs.1 | |
tfr1onlemssrecs.x |
Ref | Expression |
---|---|
tfr1onlemssrecs | recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfr1onlemssrecs.1 | . . . 4 | |
2 | tfr1onlemssrecs.x | . . . . . 6 | |
3 | ordsson 4378 | . . . . . 6 | |
4 | ssrexv 3132 | . . . . . 6 | |
5 | 2, 3, 4 | 3syl 17 | . . . . 5 |
6 | 5 | ss2abdv 3140 | . . . 4 |
7 | 1, 6 | eqsstrid 3113 | . . 3 |
8 | 7 | unissd 3730 | . 2 |
9 | df-recs 6170 | . 2 recs | |
10 | 8, 9 | sseqtrrdi 3116 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 cab 2103 wral 2393 wrex 2394 wss 3041 cuni 3706 word 4254 con0 4255 cres 4511 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-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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-in 3047 df-ss 3054 df-uni 3707 df-tr 3997 df-iord 4258 df-on 4260 df-recs 6170 |
This theorem is referenced by: tfr1onlembfn 6209 tfr1onlemubacc 6211 tfr1onlemres 6214 |
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