Theorem reu6i 3290

Description: A condition which implies existential uniqueness. (Contributed by Mario Carneiro, 2-Oct-2015.)

Assertion

Ref	Expression
reu6i

Distinct variable groups:   ,   ,

Proof of Theorem reu6i

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		eqeq2 2472	. . . . 5
2	1	bibi2d 318	. . . 4
3	2	ralbidv 2896	. . 3
4	3	rspcev 3210	. 2
5		reu6 3288	. 2
6	4, 5	sylibr 212	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  A.wral 2807  E.wrex 2808  E!wreu 2809

This theorem is referenced by:  eqreu  3291  riota5f  6282  negeu  9833  creur  10555  creui  10556  reuccats1  12706  lublecl  15619  dfod2  16586  lmieu  24150

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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-reu 2814  df-v 3111