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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 5310 |
. . . 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 5523 |
. . . . . 6
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6 | 3, 4 | reseq12d 4909 |
. . . . . . 7
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7 | 6 | fveq2d 5520 |
. . . . . 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 2711 |
. . . 4
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12 | 2, 11 | anbi12d 473 |
. . 3
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13 | 12 | cbvrexdva 2714 |
. 2
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14 | tfrlem3.1 |
. 2
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15 | 1, 13, 14 | elab2 2886 |
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 2740 df-un 3134 df-in 3136 df-ss 3143 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-br 4005 df-opab 4066 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-res 4639 df-iota 5179 df-fun 5219 df-fn 5220 df-fv 5225 |
This theorem is referenced by: tfrlem3 6312 tfrlem5 6315 tfrlemisucaccv 6326 tfrlemibxssdm 6328 tfrlemi14d 6334 tfrexlem 6335 |
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