Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > uniexg | Unicode version |
Description: The ZF Axiom of Union in class notation, in the form of a theorem instead of an inference. We use the antecedent instead of to make the theorem more general and thus shorten some proofs; obviously the universal class constant is one possible substitution for class variable . (Contributed by NM, 25-Nov-1994.) |
Ref | Expression |
---|---|
uniexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unieq 3589 | . . 3 | |
2 | 1 | eleq1d 2106 | . 2 |
3 | vex 2560 | . . 3 | |
4 | 3 | uniex 4174 | . 2 |
5 | 2, 4 | vtoclg 2613 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 cvv 2557 cuni 3580 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-un 4170 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-uni 3581 |
This theorem is referenced by: snnex 4181 uniexb 4205 ssonuni 4214 dmexg 4596 rnexg 4597 elxp4 4808 elxp5 4809 relrnfvex 5193 fvexg 5194 sefvex 5196 riotaexg 5472 iunexg 5746 1stvalg 5769 2ndvalg 5770 cnvf1o 5846 brtpos2 5866 tfrlemiex 5945 en1bg 6280 en1uniel 6284 |
Copyright terms: Public domain | W3C validator |