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Mirrors > Home > ILE Home > Th. List > tfrlem3a | Unicode version |
Description: Lemma for transfinite
recursion. Let ![]() ![]() |
Ref | Expression |
---|---|
tfrlem3.1 |
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tfrlem3.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
tfrlem3a |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfrlem3.2 |
. 2
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2 | fneq12 5328 |
. . . 4
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3 | simpll 527 |
. . . . . . 7
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4 | simpr 110 |
. . . . . . 7
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5 | 3, 4 | fveq12d 5541 |
. . . . . 6
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6 | 3, 4 | reseq12d 4926 |
. . . . . . 7
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7 | 6 | fveq2d 5538 |
. . . . . 6
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8 | 5, 7 | eqeq12d 2204 |
. . . . 5
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9 | simpr 110 |
. . . . . 6
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10 | 9 | adantr 276 |
. . . . 5
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11 | 8, 10 | cbvraldva2 2725 |
. . . 4
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12 | 2, 11 | anbi12d 473 |
. . 3
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13 | 12 | cbvrexdva 2728 |
. 2
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14 | tfrlem3.1 |
. 2
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15 | 1, 13, 14 | elab2 2900 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-res 4656 df-iota 5196 df-fun 5237 df-fn 5238 df-fv 5243 |
This theorem is referenced by: tfrlem3 6337 tfrlem5 6340 tfrlemisucaccv 6351 tfrlemibxssdm 6353 tfrlemi14d 6359 tfrexlem 6360 |
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