Theorem int0OLD 4491

Description: Obsolete proof of int0 4490 as of 26-Jul-2021. (Contributed by NM, 18-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
int0OLD	|- |^| (/) = _V

Proof of Theorem int0OLD

Dummy variables x y are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		noel 3919	. . . . . 6 |- -. y e. (/)
2	1	pm2.21i 116	. . . . 5 |- ( y e. (/) -> x e. y )
3	2	ax-gen 1722	. . . 4 |- A. y ( y e. (/) -> x e. y )
4		equid 1939	. . . 4 |- x = x
5	3, 4	2th 254	. . 3 |- ( A. y ( y e. (/) -> x e. y ) <-> x = x )
6	5	abbii 2739	. 2 |- { x | A. y ( y e. (/) -> x e. y ) } = { x | x = x }
7		df-int 4476	. 2 |- |^| (/) = { x | A. y ( y e. (/) -> x e. y ) }
8		df-v 3202	. 2 |- _V = { x | x = x }
9	6, 7, 8	3eqtr4i 2654	1 |- |^| (/) = _V

Syntax hints:   -> wi 4   A.wal 1481   = wceq 1483   e. wcel 1990   {cab 2608   _Vcvv 3200   (/)c0 3915   |^|cint 4475

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-nul 3916  df-int 4476

This theorem is referenced by: (None)