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Mirrors > Home > ILE Home > Th. List > ltdfpr | Unicode version |
Description: More convenient form of df-iltp 7432. (Contributed by Jim Kingdon, 15-Dec-2019.) |
Ref | Expression |
---|---|
ltdfpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3990 | . . 3 | |
2 | df-iltp 7432 | . . . 4 | |
3 | 2 | eleq2i 2237 | . . 3 |
4 | 1, 3 | bitri 183 | . 2 |
5 | simpl 108 | . . . . . . 7 | |
6 | 5 | fveq2d 5500 | . . . . . 6 |
7 | 6 | eleq2d 2240 | . . . . 5 |
8 | simpr 109 | . . . . . . 7 | |
9 | 8 | fveq2d 5500 | . . . . . 6 |
10 | 9 | eleq2d 2240 | . . . . 5 |
11 | 7, 10 | anbi12d 470 | . . . 4 |
12 | 11 | rexbidv 2471 | . . 3 |
13 | 12 | opelopab2a 4250 | . 2 |
14 | 4, 13 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wcel 2141 wrex 2449 cop 3586 class class class wbr 3989 copab 4049 cfv 5198 c1st 6117 c2nd 6118 cnq 7242 cnp 7253 cltp 7257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-iota 5160 df-fv 5206 df-iltp 7432 |
This theorem is referenced by: nqprl 7513 nqpru 7514 ltprordil 7551 ltnqpr 7555 ltnqpri 7556 ltpopr 7557 ltsopr 7558 ltaddpr 7559 ltexprlemm 7562 ltexprlemopu 7565 ltexprlemru 7574 aptiprleml 7601 aptiprlemu 7602 archpr 7605 cauappcvgprlem2 7622 caucvgprlem2 7642 caucvgprprlemopu 7661 caucvgprprlemexbt 7668 caucvgprprlem2 7672 suplocexprlemloc 7683 suplocexprlemub 7685 suplocexprlemlub 7686 |
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