Theorem eubid 2302

Description: Formula-building rule for uniqueness quantifier (deduction rule). (Contributed by NM, 9-Jul-1994.)

Hypotheses

Ref	Expression
eubid.1
eubid.2

Assertion

Ref	Expression
eubid

Proof of Theorem eubid

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		eubid.1	. . . 4
2		eubid.2	. . . . 5
3	2	bibi1d 319	. . . 4
4	1, 3	albid 1885	. . 3
5	4	exbidv 1714	. 2
6		df-eu 2286	. 2
7		df-eu 2286	. 2
8	5, 6, 7	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616  E!weu 2282

This theorem is referenced by:  mobid  2303  eubidv  2304  euor  2331  euor2  2333  euan  2351  reubida  3040  reueq1f  3052  eusv2i  4649  reusv2lem3  4655  eubi  31343

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-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617  df-eu 2286