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Mirrors > Home > MPE Home > Th. List > df-ac | Structured version Visualization version Unicode version |
Description: The expression
CHOICE will be used as a readable shorthand for any
form of the axiom of choice; all concrete forms are long, cryptic, have
dummy variables, or all three, making it useful to have a short name.
Similar to the Axiom of Choice (first form) of [Enderton] p. 49.
There is a slight problem with taking the exact form of ax-ac 8915 as our definition, because the equivalence to more standard forms (dfac2 8587) requires the Axiom of Regularity, which we often try to avoid. Thus, we take the first of the "textbook forms" as the definition and derive the form of ax-ac 8915 itself as dfac0 8589. (Contributed by Mario Carneiro, 22-Feb-2015.) |
Ref | Expression |
---|---|
df-ac | CHOICE |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wac 8572 | . 2 CHOICE | |
2 | vf | . . . . . . 7 | |
3 | 2 | cv 1454 | . . . . . 6 |
4 | vx | . . . . . . 7 | |
5 | 4 | cv 1454 | . . . . . 6 |
6 | 3, 5 | wss 3416 | . . . . 5 |
7 | 5 | cdm 4853 | . . . . . 6 |
8 | 3, 7 | wfn 5596 | . . . . 5 |
9 | 6, 8 | wa 375 | . . . 4 |
10 | 9, 2 | wex 1674 | . . 3 |
11 | 10, 4 | wal 1453 | . 2 |
12 | 1, 11 | wb 189 | 1 CHOICE |
Colors of variables: wff setvar class |
This definition is referenced by: dfac3 8578 ac7 8929 |
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