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Mirrors > Home > MPE Home > Th. List > Mathboxes > supex2g | Structured version Visualization version Unicode version |
Description: Existence of supremum. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
supex2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sup 8348 | . 2 | |
2 | rabexg 4812 | . . 3 | |
3 | uniexg 6955 | . . 3 | |
4 | 2, 3 | syl 17 | . 2 |
5 | 1, 4 | syl5eqel 2705 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wcel 1990 wral 2912 wrex 2913 crab 2916 cvv 3200 cuni 4436 class class class wbr 4653 csup 8346 |
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-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-rab 2921 df-v 3202 df-in 3581 df-ss 3588 df-uni 4437 df-sup 8348 |
This theorem is referenced by: (None) |
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