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Mirrors > Home > ILE Home > Th. List > rnpropg | Unicode version |
Description: The range of a pair of ordered pairs is the pair of second members. (Contributed by Thierry Arnoux, 3-Jan-2017.) |
Ref | Expression |
---|---|
rnpropg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pr 3504 | . . 3 | |
2 | 1 | rneqi 4737 | . 2 |
3 | rnsnopg 4987 | . . . . 5 | |
4 | 3 | adantr 274 | . . . 4 |
5 | rnsnopg 4987 | . . . . 5 | |
6 | 5 | adantl 275 | . . . 4 |
7 | 4, 6 | uneq12d 3201 | . . 3 |
8 | rnun 4917 | . . 3 | |
9 | df-pr 3504 | . . 3 | |
10 | 7, 8, 9 | 3eqtr4g 2175 | . 2 |
11 | 2, 10 | syl5eq 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cun 3039 csn 3497 cpr 3498 cop 3500 crn 4510 |
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-ral 2398 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-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-dm 4519 df-rn 4520 |
This theorem is referenced by: (None) |
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