Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opswapg | Unicode version |
Description: Swap the members of an ordered pair. (Contributed by Jim Kingdon, 16-Dec-2018.) |
Ref | Expression |
---|---|
opswapg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvsng 4994 | . . 3 | |
2 | 1 | unieqd 3717 | . 2 |
3 | elex 2671 | . . . 4 | |
4 | elex 2671 | . . . 4 | |
5 | opexg 4120 | . . . 4 | |
6 | 3, 4, 5 | syl2anr 288 | . . 3 |
7 | unisng 3723 | . . 3 | |
8 | 6, 7 | syl 14 | . 2 |
9 | 2, 8 | eqtrd 2150 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 cvv 2660 csn 3497 cop 3500 cuni 3706 ccnv 4508 |
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-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 |
This theorem is referenced by: 2nd1st 6046 cnvf1olem 6089 brtposg 6119 dftpos4 6128 tpostpos 6129 xpcomco 6688 fsumcnv 11174 txswaphmeolem 12416 |
Copyright terms: Public domain | W3C validator |