Theorem eusv1 4646

Description: Two ways to express single-valuedness of a class expression A(x). (Contributed by NM, 14-Oct-2010.)

Assertion

Ref	Expression
eusv1

Distinct variable groups:   ,   ,

Proof of Theorem eusv1

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		sp 1859	. . . 4
2		sp 1859	. . . 4
3		eqtr3 2485	. . . 4
4	1, 2, 3	syl2an 477	. . 3
5	4	gen2 1619	. 2
6		eqeq1 2461	. . . 4
7	6	albidv 1713	. . 3
8	7	eu4 2338	. 2
9	5, 8	mpbiran2 919	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  E!weu 2282

This theorem is referenced by:  eusvnfb  4648

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-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-cleq 2449