Theorem eldmg 5203

Description: Domain membership. Theorem 4 of [Suppes] p. 59. (Contributed by Mario Carneiro, 9-Jul-2014.)

Assertion

Ref	Expression
eldmg

Distinct variable groups:   ,   ,

Proof of Theorem eldmg

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		breq1 4455	. . 3
2	1	exbidv 1714	. 2
3		df-dm 5014	. 2
4	2, 3	elab2g 3248	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wex 1612  e.wcel 1818   class class class wbr 4452  domcdm 5004

This theorem is referenced by:  eldm2g  5204  eldm  5205  breldmg  5213  releldmb  5242  funeu  5617  fneu  5690  ndmfv  5895  erref  7350  ecdmn0  7373  rlimdm  13374  rlimdmo1  13440  iscmet3lem2  21731  dvcnp2  22323  ulmcau  22790  pserulm  22817  mulog2sum  23722  afveu  32238  rlimdmafv  32262

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-dm 5014