Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > relresfld | Unicode version |
Description: Restriction of a relation to its field. (Contributed by FL, 15-Apr-2012.) |
Ref | Expression |
---|---|
relresfld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relfld 5126 | . . . 4 | |
2 | 1 | reseq2d 4878 | . . 3 |
3 | resundi 4891 | . . 3 | |
4 | eqtr 2182 | . . . 4 | |
5 | resss 4902 | . . . . 5 | |
6 | resdm 4917 | . . . . 5 | |
7 | ssequn2 3290 | . . . . . 6 | |
8 | uneq1 3264 | . . . . . . . . 9 | |
9 | 8 | eqeq2d 2176 | . . . . . . . 8 |
10 | eqtr 2182 | . . . . . . . . 9 | |
11 | 10 | ex 114 | . . . . . . . 8 |
12 | 9, 11 | syl6bi 162 | . . . . . . 7 |
13 | 12 | com3r 79 | . . . . . 6 |
14 | 7, 13 | sylbi 120 | . . . . 5 |
15 | 5, 6, 14 | mpsyl 65 | . . . 4 |
16 | 4, 15 | syl5com 29 | . . 3 |
17 | 2, 3, 16 | sylancl 410 | . 2 |
18 | 17 | pm2.43i 49 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 cun 3109 wss 3111 cuni 3783 cdm 4598 crn 4599 cres 4600 wrel 4603 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-cnv 4606 df-dm 4608 df-rn 4609 df-res 4610 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |