Theorem 19.42vvv 1778

Description: Version of 19.42 1972 with three quantifiers and a dv condition requiring fewer axioms. (Contributed by NM, 21-Sep-2011.)

Assertion

Ref	Expression
19.42vvv

Distinct variable groups:   ,   ,   ,

Proof of Theorem 19.42vvv

Step	Hyp	Ref	Expression
1		19.42vv 1777	. . 3
2	1	exbii 1667	. 2
3		19.42v 1775	. 2
4	2, 3	bitri 249	1

Syntax hints:  <->wb 184  /\wa 369  E.wex 1612

This theorem is referenced by:  ceqsex6v  3151

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613