Theorem dfral2 2904

Description: Relationship between restricted universal and existential quantifiers. (Contributed by NM, 21-Jan-1997.) Allow shortening of rexnal 2905. (Revised by Wolf Lammen, 9-Dec-2019.)

Assertion

Ref	Expression
dfral2

Proof of Theorem dfral2

Step	Hyp	Ref	Expression
1		notnot 291	. . 3
2	1	ralbii 2888	. 2
3		ralnex 2903	. 2
4	2, 3	bitri 249	1

Syntax hints:  -.wn 3  <->wb 184  A.wral 2807  E.wrex 2808

This theorem is referenced by:  rexnal  2905  boxcutc  7532  infssuni  7831  ac6n  8886  indstr  11179  trfil3  20389  tglowdim2ln  24032  nmobndseqi  25694  stri  27176  hstri  27184  bnj1204  34068

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-ral 2812  df-rex 2813