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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 5152 |
. . . 4
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3 | simpll 499 |
. . . . . . 7
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4 | simpr 109 |
. . . . . . 7
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5 | 3, 4 | fveq12d 5360 |
. . . . . 6
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6 | 3, 4 | reseq12d 4756 |
. . . . . . 7
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7 | 6 | fveq2d 5357 |
. . . . . 6
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8 | 5, 7 | eqeq12d 2114 |
. . . . 5
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9 | simpr 109 |
. . . . . 6
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10 | 9 | adantr 272 |
. . . . 5
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11 | 8, 10 | cbvraldva2 2616 |
. . . 4
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12 | 2, 11 | anbi12d 460 |
. . 3
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13 | 12 | cbvrexdva 2619 |
. 2
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14 | tfrlem3.1 |
. 2
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15 | 1, 13, 14 | elab2 2785 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-xp 4483 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-res 4489 df-iota 5024 df-fun 5061 df-fn 5062 df-fv 5067 |
This theorem is referenced by: tfrlem3 6138 tfrlem5 6141 tfrlemisucaccv 6152 tfrlemibxssdm 6154 tfrlemi14d 6160 tfrexlem 6161 |
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