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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 5304 |
. . . 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 5517 |
. . . . . 6
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6 | 3, 4 | reseq12d 4903 |
. . . . . . 7
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7 | 6 | fveq2d 5514 |
. . . . . 6
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8 | 5, 7 | eqeq12d 2192 |
. . . . 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 2710 |
. . . 4
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12 | 2, 11 | anbi12d 473 |
. . 3
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13 | 12 | cbvrexdva 2713 |
. 2
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14 | tfrlem3.1 |
. 2
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15 | 1, 13, 14 | elab2 2885 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-res 4634 df-iota 5173 df-fun 5213 df-fn 5214 df-fv 5219 |
This theorem is referenced by: tfrlem3 6305 tfrlem5 6308 tfrlemisucaccv 6319 tfrlemibxssdm 6321 tfrlemi14d 6327 tfrexlem 6328 |
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