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Mirrors > Home > ILE Home > Th. List > ltdfpr | Unicode version |
Description: More convenient form of df-iltp 7246. (Contributed by Jim Kingdon, 15-Dec-2019.) |
Ref | Expression |
---|---|
ltdfpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3900 | . . 3 | |
2 | df-iltp 7246 | . . . 4 | |
3 | 2 | eleq2i 2184 | . . 3 |
4 | 1, 3 | bitri 183 | . 2 |
5 | simpl 108 | . . . . . . 7 | |
6 | 5 | fveq2d 5393 | . . . . . 6 |
7 | 6 | eleq2d 2187 | . . . . 5 |
8 | simpr 109 | . . . . . . 7 | |
9 | 8 | fveq2d 5393 | . . . . . 6 |
10 | 9 | eleq2d 2187 | . . . . 5 |
11 | 7, 10 | anbi12d 464 | . . . 4 |
12 | 11 | rexbidv 2415 | . . 3 |
13 | 12 | opelopab2a 4157 | . 2 |
14 | 4, 13 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wcel 1465 wrex 2394 cop 3500 class class class wbr 3899 copab 3958 cfv 5093 c1st 6004 c2nd 6005 cnq 7056 cnp 7067 cltp 7071 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-iota 5058 df-fv 5101 df-iltp 7246 |
This theorem is referenced by: nqprl 7327 nqpru 7328 ltprordil 7365 ltnqpr 7369 ltnqpri 7370 ltpopr 7371 ltsopr 7372 ltaddpr 7373 ltexprlemm 7376 ltexprlemopu 7379 ltexprlemru 7388 aptiprleml 7415 aptiprlemu 7416 archpr 7419 cauappcvgprlem2 7436 caucvgprlem2 7456 caucvgprprlemopu 7475 caucvgprprlemexbt 7482 caucvgprprlem2 7486 suplocexprlemloc 7497 suplocexprlemub 7499 suplocexprlemlub 7500 |
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