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Mirrors > Home > ILE Home > Th. List > ltdfpr | Unicode version |
Description: More convenient form of df-iltp 6774. (Contributed by Jim Kingdon, 15-Dec-2019.) |
Ref | Expression |
---|---|
ltdfpr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3806 |
. . 3
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2 | df-iltp 6774 |
. . . 4
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3 | 2 | eleq2i 2149 |
. . 3
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4 | 1, 3 | bitri 182 |
. 2
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5 | simpl 107 |
. . . . . . 7
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6 | 5 | fveq2d 5233 |
. . . . . 6
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7 | 6 | eleq2d 2152 |
. . . . 5
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8 | simpr 108 |
. . . . . . 7
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9 | 8 | fveq2d 5233 |
. . . . . 6
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10 | 9 | eleq2d 2152 |
. . . . 5
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11 | 7, 10 | anbi12d 457 |
. . . 4
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12 | 11 | rexbidv 2374 |
. . 3
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13 | 12 | opelopab2a 4048 |
. 2
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14 | 4, 13 | syl5bb 190 |
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-14 1446 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 ax-sep 3916 ax-pow 3968 ax-pr 3992 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-eu 1946 df-mo 1947 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-rex 2359 df-v 2612 df-un 2986 df-in 2988 df-ss 2995 df-pw 3402 df-sn 3422 df-pr 3423 df-op 3425 df-uni 3622 df-br 3806 df-opab 3860 df-iota 4917 df-fv 4960 df-iltp 6774 |
This theorem is referenced by: nqprl 6855 nqpru 6856 ltprordil 6893 ltnqpr 6897 ltnqpri 6898 ltpopr 6899 ltsopr 6900 ltaddpr 6901 ltexprlemm 6904 ltexprlemopu 6907 ltexprlemru 6916 aptiprleml 6943 aptiprlemu 6944 archpr 6947 cauappcvgprlem2 6964 caucvgprlem2 6984 caucvgprprlemopu 7003 caucvgprprlemexbt 7010 caucvgprprlem2 7014 |
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