Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > uniqs2 | Unicode version |
Description: The union of a quotient set. (Contributed by Mario Carneiro, 11-Jul-2014.) |
Ref | Expression |
---|---|
qsss.1 | |
qsss.2 |
Ref | Expression |
---|---|
uniqs2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qsss.2 | . . . . 5 | |
2 | uniqs 6487 | . . . . 5 | |
3 | 1, 2 | syl 14 | . . . 4 |
4 | qsss.1 | . . . . . 6 | |
5 | erdm 6439 | . . . . . 6 | |
6 | 4, 5 | syl 14 | . . . . 5 |
7 | 6 | imaeq2d 4881 | . . . 4 |
8 | 3, 7 | eqtr4d 2175 | . . 3 |
9 | imadmrn 4891 | . . 3 | |
10 | 8, 9 | syl6eq 2188 | . 2 |
11 | errn 6451 | . . 3 | |
12 | 4, 11 | syl 14 | . 2 |
13 | 10, 12 | eqtrd 2172 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cuni 3736 cdm 4539 crn 4540 cima 4542 wer 6426 cqs 6428 |
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-13 1491 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 ax-un 4355 |
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-ral 2421 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-iun 3815 df-br 3930 df-opab 3990 df-xp 4545 df-rel 4546 df-cnv 4547 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-er 6429 df-ec 6431 df-qs 6435 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |