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Mirrors > Home > ILE Home > Th. List > tfrlem3 | Unicode version |
Description: Lemma for transfinite recursion. Let be the class of "acceptable" functions. The final thing we're interested in is the union of all these acceptable functions. This lemma just changes some bound variables in for later use. (Contributed by NM, 9-Apr-1995.) |
Ref | Expression |
---|---|
tfrlem3.1 |
Ref | Expression |
---|---|
tfrlem3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlem3.1 | . . 3 | |
2 | vex 2733 | . . 3 | |
3 | 1, 2 | tfrlem3a 6289 | . 2 |
4 | 3 | abbi2i 2285 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 cab 2156 wral 2448 wrex 2449 con0 4348 cres 4613 wfn 5193 cfv 5198 |
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-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-res 4623 df-iota 5160 df-fun 5200 df-fn 5201 df-fv 5206 |
This theorem is referenced by: tfrlem4 6292 tfrlem8 6297 tfrlemi1 6311 tfrexlem 6313 tfri1d 6314 tfrex 6347 |
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