Theorem ralbiim 2989

Description: Split a biconditional and distribute quantifier. Restricted quantifier version of albiim 1699. (Contributed by NM, 3-Jun-2012.)

Assertion

Ref	Expression
ralbiim

Proof of Theorem ralbiim

Step	Hyp	Ref	Expression
1		dfbi2 628	. . 3
2	1	ralbii 2888	. 2
3		r19.26 2984	. 2
4	2, 3	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wral 2807

This theorem is referenced by:  eqreu  3291  isclo2  19589  chrelat4i  27292  2ralbiim  32179  hlateq  35123

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-ral 2812