Theorem brsdom 7558

Description: Strict dominance relation, meaning " is strictly greater in size than ." Definition of [Mendelson] p. 255. (Contributed by NM, 25-Jun-1998.)

Assertion

Ref	Expression
brsdom

Proof of Theorem brsdom

Step	Hyp	Ref	Expression
1		df-sdom 7539	. . 3
2	1	eleq2i 2535	. 2
3		df-br 4453	. 2
4		df-br 4453	. . . 4
5		df-br 4453	. . . . 5
6	5	notbii 296	. . . 4
7	4, 6	anbi12i 697	. . 3
8		eldif 3485	. . 3
9	7, 8	bitr4i 252	. 2
10	2, 3, 9	3bitr4i 277	1

Syntax hints:  -.wn 3  <->wb 184  /\wa 369  e.wcel 1818  \cdif 3472  <.cop 4035   class class class wbr 4452  cen 7533  cdom 7534  csdm 7535

This theorem is referenced by:  sdomdom  7563  sdomnen  7564  0sdomg  7666  sdomdomtr  7670  domsdomtr  7672  domtriord  7683  canth2  7690  php2  7722  php3  7723  nnsdomo  7732  nnsdomg  7799  card2inf  8002  cardsdomelir  8375  cardsdom2  8390  fidomtri2  8396  cardmin2  8400  alephordi  8476  alephord  8477  isfin4-3  8716  isfin5-2  8792  canthnum  9048  canthwe  9050  canthp1  9053  gchcdaidm  9067  gchxpidm  9068  gchhar  9078  axgroth6  9227  hashsdom  12449  ruc  13976

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-an 371  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-v 3111  df-dif 3478  df-br 4453  df-sdom 7539