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Mirrors > Home > MPE Home > Th. List > zfun | Structured version Visualization version Unicode version |
Description: Axiom of Union expressed with the fewest number of different variables. (Contributed by NM, 14-Aug-2003.) |
Ref | Expression |
---|---|
zfun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-un 6949 | . 2 | |
2 | elequ2 2004 | . . . . . . 7 | |
3 | elequ1 1997 | . . . . . . 7 | |
4 | 2, 3 | anbi12d 747 | . . . . . 6 |
5 | 4 | cbvexv 2275 | . . . . 5 |
6 | 5 | imbi1i 339 | . . . 4 |
7 | 6 | albii 1747 | . . 3 |
8 | 7 | exbii 1774 | . 2 |
9 | 1, 8 | mpbi 220 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wex 1704 |
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-11 2034 ax-12 2047 ax-13 2246 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: uniex2 6952 axunndlem1 9417 |
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