Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ac Unicode version

Definition df-ac 8518
 Description: The expression 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 8860 as our definition, because the equivalence to more standard forms (dfac2 8532) 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 8860 itself as dfac0 8534. (Contributed by Mario Carneiro, 22-Feb-2015.)
Assertion
Ref Expression
df-ac
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-ac
StepHypRef Expression
1 wac 8517 . 2
2 vf . . . . . . 7
32cv 1394 . . . . . 6
4 vx . . . . . . 7
54cv 1394 . . . . . 6
63, 5wss 3475 . . . . 5
75cdm 5004 . . . . . 6
83, 7wfn 5588 . . . . 5
96, 8wa 369 . . . 4
109, 2wex 1612 . . 3
1110, 4wal 1393 . 2
121, 11wb 184 1
 Colors of variables: wff setvar class This definition is referenced by:  dfac3  8523  ac7  8874
 Copyright terms: Public domain W3C validator