Theorem reupick3 3782

Description: Restricted uniqueness "picks" a member of a subclass. (Contributed by Mario Carneiro, 19-Nov-2016.)

Assertion

Ref	Expression
reupick3

Distinct variable group:   ,

Proof of Theorem reupick3

Step	Hyp	Ref	Expression
1		df-reu 2814	. . . 4
2		df-rex 2813	. . . . 5
3		anass 649	. . . . . 6
4	3	exbii 1667	. . . . 5
5	2, 4	bitr4i 252	. . . 4
6		eupick 2358	. . . 4
7	1, 5, 6	syl2anb 479	. . 3
8	7	expd 436	. 2
9	8	3impia 1193	1

Syntax hints:  ->wi 4  /\wa 369  /\w3a 973  E.wex 1612  e.wcel 1818  E!weu 2282  E.wrex 2808  E!wreu 2809

This theorem is referenced by:  reupick2  3783

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-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-rex 2813  df-reu 2814