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Mirrors > Home > ILE Home > Th. List > ltdfpr | Unicode version |
Description: More convenient form of df-iltp 7390. (Contributed by Jim Kingdon, 15-Dec-2019.) |
Ref | Expression |
---|---|
ltdfpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3966 | . . 3 | |
2 | df-iltp 7390 | . . . 4 | |
3 | 2 | eleq2i 2224 | . . 3 |
4 | 1, 3 | bitri 183 | . 2 |
5 | simpl 108 | . . . . . . 7 | |
6 | 5 | fveq2d 5472 | . . . . . 6 |
7 | 6 | eleq2d 2227 | . . . . 5 |
8 | simpr 109 | . . . . . . 7 | |
9 | 8 | fveq2d 5472 | . . . . . 6 |
10 | 9 | eleq2d 2227 | . . . . 5 |
11 | 7, 10 | anbi12d 465 | . . . 4 |
12 | 11 | rexbidv 2458 | . . 3 |
13 | 12 | opelopab2a 4225 | . 2 |
14 | 4, 13 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 wrex 2436 cop 3563 class class class wbr 3965 copab 4024 cfv 5170 c1st 6086 c2nd 6087 cnq 7200 cnp 7211 cltp 7215 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-iota 5135 df-fv 5178 df-iltp 7390 |
This theorem is referenced by: nqprl 7471 nqpru 7472 ltprordil 7509 ltnqpr 7513 ltnqpri 7514 ltpopr 7515 ltsopr 7516 ltaddpr 7517 ltexprlemm 7520 ltexprlemopu 7523 ltexprlemru 7532 aptiprleml 7559 aptiprlemu 7560 archpr 7563 cauappcvgprlem2 7580 caucvgprlem2 7600 caucvgprprlemopu 7619 caucvgprprlemexbt 7626 caucvgprprlem2 7630 suplocexprlemloc 7641 suplocexprlemub 7643 suplocexprlemlub 7644 |
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