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Mirrors > Home > ILE Home > Th. List > tfrcllemssrecs | Unicode version |
Description: Lemma for tfrcl 6340. The union of functions acceptable for tfrcl 6340 is a subset of recs. (Contributed by Jim Kingdon, 25-Mar-2022.) |
Ref | Expression |
---|---|
tfrcllemssrecs.1 | |
tfrcllemssrecs.x |
Ref | Expression |
---|---|
tfrcllemssrecs | recs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrcllemssrecs.1 | . . . 4 | |
2 | tfrcllemssrecs.x | . . . . . 6 | |
3 | ordsson 4474 | . . . . . 6 | |
4 | ssrexv 3212 | . . . . . 6 | |
5 | 2, 3, 4 | 3syl 17 | . . . . 5 |
6 | 5 | ss2abdv 3220 | . . . 4 |
7 | 1, 6 | eqsstrid 3193 | . . 3 |
8 | 7 | unissd 3818 | . 2 |
9 | ffn 5345 | . . . . . . 7 | |
10 | 9 | anim1i 338 | . . . . . 6 |
11 | 10 | reximi 2567 | . . . . 5 |
12 | 11 | ss2abi 3219 | . . . 4 |
13 | 12 | unissi 3817 | . . 3 |
14 | df-recs 6281 | . . 3 recs | |
15 | 13, 14 | sseqtrri 3182 | . 2 recs |
16 | 8, 15 | sstrdi 3159 | 1 recs |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 cab 2156 wral 2448 wrex 2449 wss 3121 cuni 3794 word 4345 con0 4346 cres 4611 wfn 5191 wf 5192 cfv 5196 recscrecs 6280 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-in 3127 df-ss 3134 df-uni 3795 df-tr 4086 df-iord 4349 df-on 4351 df-f 5200 df-recs 6281 |
This theorem is referenced by: tfrcllembfn 6333 tfrcllemubacc 6335 tfrcllemres 6338 |
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