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Mirrors > Home > ILE Home > Th. List > tfrlem4 | Unicode version |
Description: Lemma for transfinite recursion. is the class of all "acceptable" functions, and is their union. First we show that an acceptable function is in fact a function. (Contributed by NM, 9-Apr-1995.) |
Ref | Expression |
---|---|
tfrlem.1 |
Ref | Expression |
---|---|
tfrlem4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlem.1 | . . . 4 | |
2 | 1 | tfrlem3 6260 | . . 3 |
3 | 2 | abeq2i 2268 | . 2 |
4 | fnfun 5269 | . . . 4 | |
5 | 4 | adantr 274 | . . 3 |
6 | 5 | rexlimivw 2570 | . 2 |
7 | 3, 6 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 cab 2143 wral 2435 wrex 2436 con0 4325 cres 4590 wfun 5166 wfn 5167 cfv 5172 |
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 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-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-res 4600 df-iota 5137 df-fun 5174 df-fn 5175 df-fv 5180 |
This theorem is referenced by: tfrlem6 6265 |
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