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Mirrors > Home > ILE Home > Th. List > tfrlem3ag | Unicode version |
Description: Lemma for transfinite
recursion. This lemma just changes some bound
variables in ![]() |
Ref | Expression |
---|---|
tfrlem3.1 |
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Ref | Expression |
---|---|
tfrlem3ag |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq12 5017 |
. . . 4
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2 | simpll 496 |
. . . . . . 7
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3 | simpr 108 |
. . . . . . 7
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4 | 2, 3 | fveq12d 5209 |
. . . . . 6
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5 | 2, 3 | reseq12d 4635 |
. . . . . . 7
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6 | 5 | fveq2d 5207 |
. . . . . 6
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7 | 4, 6 | eqeq12d 2096 |
. . . . 5
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8 | simplr 497 |
. . . . 5
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9 | 7, 8 | cbvraldva2 2582 |
. . . 4
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10 | 1, 9 | anbi12d 457 |
. . 3
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11 | 10 | cbvrexdva 2585 |
. 2
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12 | tfrlem3.1 |
. 2
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13 | 11, 12 | elab2g 2741 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-ral 2354 df-rex 2355 df-v 2604 df-un 2978 df-in 2980 df-ss 2987 df-sn 3406 df-pr 3407 df-op 3409 df-uni 3604 df-br 3788 df-opab 3842 df-xp 4371 df-rel 4372 df-cnv 4373 df-co 4374 df-dm 4375 df-res 4377 df-iota 4891 df-fun 4928 df-fn 4929 df-fv 4934 |
This theorem is referenced by: tfrlemisucaccv 5968 |
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