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Mirrors > Home > ILE Home > Th. List > ltdfpr | Unicode version |
Description: More convenient form of df-iltp 7281. (Contributed by Jim Kingdon, 15-Dec-2019.) |
Ref | Expression |
---|---|
ltdfpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 3930 | . . 3 | |
2 | df-iltp 7281 | . . . 4 | |
3 | 2 | eleq2i 2206 | . . 3 |
4 | 1, 3 | bitri 183 | . 2 |
5 | simpl 108 | . . . . . . 7 | |
6 | 5 | fveq2d 5425 | . . . . . 6 |
7 | 6 | eleq2d 2209 | . . . . 5 |
8 | simpr 109 | . . . . . . 7 | |
9 | 8 | fveq2d 5425 | . . . . . 6 |
10 | 9 | eleq2d 2209 | . . . . 5 |
11 | 7, 10 | anbi12d 464 | . . . 4 |
12 | 11 | rexbidv 2438 | . . 3 |
13 | 12 | opelopab2a 4187 | . 2 |
14 | 4, 13 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wrex 2417 cop 3530 class class class wbr 3929 copab 3988 cfv 5123 c1st 6036 c2nd 6037 cnq 7091 cnp 7102 cltp 7106 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-iota 5088 df-fv 5131 df-iltp 7281 |
This theorem is referenced by: nqprl 7362 nqpru 7363 ltprordil 7400 ltnqpr 7404 ltnqpri 7405 ltpopr 7406 ltsopr 7407 ltaddpr 7408 ltexprlemm 7411 ltexprlemopu 7414 ltexprlemru 7423 aptiprleml 7450 aptiprlemu 7451 archpr 7454 cauappcvgprlem2 7471 caucvgprlem2 7491 caucvgprprlemopu 7510 caucvgprprlemexbt 7517 caucvgprprlem2 7521 suplocexprlemloc 7532 suplocexprlemub 7534 suplocexprlemlub 7535 |
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