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Mirrors > Home > ILE Home > Th. List > ltdfpr | Unicode version |
Description: More convenient form of df-iltp 7466. (Contributed by Jim Kingdon, 15-Dec-2019.) |
Ref | Expression |
---|---|
ltdfpr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 4003 |
. . 3
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2 | df-iltp 7466 |
. . . 4
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3 | 2 | eleq2i 2244 |
. . 3
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4 | 1, 3 | bitri 184 |
. 2
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5 | simpl 109 |
. . . . . . 7
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6 | 5 | fveq2d 5518 |
. . . . . 6
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7 | 6 | eleq2d 2247 |
. . . . 5
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8 | simpr 110 |
. . . . . . 7
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9 | 8 | fveq2d 5518 |
. . . . . 6
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10 | 9 | eleq2d 2247 |
. . . . 5
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11 | 7, 10 | anbi12d 473 |
. . . 4
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12 | 11 | rexbidv 2478 |
. . 3
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13 | 12 | opelopab2a 4264 |
. 2
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14 | 4, 13 | bitrid 192 |
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-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rex 2461 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-iota 5177 df-fv 5223 df-iltp 7466 |
This theorem is referenced by: nqprl 7547 nqpru 7548 ltprordil 7585 ltnqpr 7589 ltnqpri 7590 ltpopr 7591 ltsopr 7592 ltaddpr 7593 ltexprlemm 7596 ltexprlemopu 7599 ltexprlemru 7608 aptiprleml 7635 aptiprlemu 7636 archpr 7639 cauappcvgprlem2 7656 caucvgprlem2 7676 caucvgprprlemopu 7695 caucvgprprlemexbt 7702 caucvgprprlem2 7706 suplocexprlemloc 7717 suplocexprlemub 7719 suplocexprlemlub 7720 |
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