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Mirrors > Home > MPE Home > Th. List > uniexb | Structured version Visualization version Unicode version |
Description: The Axiom of Union and its converse. A class is a set iff its union is a set. (Contributed by NM, 11-Nov-2003.) |
Ref | Expression |
---|---|
uniexb |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uniexg 6955 | . 2 | |
2 | uniexr 6972 | . 2 | |
3 | 1, 2 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wcel 1990 cvv 3200 cuni 4436 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-pow 4843 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-v 3202 df-in 3581 df-ss 3588 df-pw 4160 df-uni 4437 |
This theorem is referenced by: ixpexg 7932 rankuni 8726 unialeph 8924 ttukeylem1 9331 tgss2 20791 ordtbas2 20995 ordtbas 20996 ordttopon 20997 ordtopn1 20998 ordtopn2 20999 ordtrest2 21008 isref 21312 islocfin 21320 txbasex 21369 ptbasin2 21381 ordthmeolem 21604 alexsublem 21848 alexsub 21849 alexsubb 21850 ussid 22064 ordtrest2NEW 29969 omsfval 30356 brbigcup 32005 isfne 32334 isfne4 32335 isfne4b 32336 fnessref 32352 neibastop1 32354 fnejoin2 32364 prtex 34165 |
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