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 3745 | . . 3 | |
2 | 1 | eleq1d 2208 | . 2 |
3 | vex 2689 | . . 3 | |
4 | 3 | uniex 4359 | . 2 |
5 | 2, 4 | vtoclg 2746 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cvv 2686 cuni 3736 |
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-un 4355 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-uni 3737 |
This theorem is referenced by: abnexg 4367 snnex 4369 uniexb 4394 ssonuni 4404 dmexg 4803 rnexg 4804 elxp4 5026 elxp5 5027 relrnfvex 5439 fvexg 5440 sefvex 5442 riotaexg 5734 iunexg 6017 1stvalg 6040 2ndvalg 6041 cnvf1o 6122 brtpos2 6148 tfrlemiex 6228 tfr1onlemex 6244 tfrcllemex 6257 en1bg 6694 en1uniel 6698 fival 6858 suplocexprlem2b 7522 suplocexprlemlub 7532 restid 12131 istopon 12180 tgval 12218 tgvalex 12219 eltg 12221 eltg2 12222 tgss2 12248 ntrval 12279 restin 12345 cnovex 12365 cnprcl2k 12375 cnptopresti 12407 cnptoprest 12408 cnptoprest2 12409 lmtopcnp 12419 txbasex 12426 uptx 12443 reldvg 12817 |
Copyright terms: Public domain | W3C validator |