Theorem bj-0nmoore 33067

Description: The empty set is not a Moore collection. (Contributed by BJ, 9-Dec-2021.)

Assertion

Ref	Expression
bj-0nmoore	|- -. (/) e. Moore_

Proof of Theorem bj-0nmoore

Step	Hyp	Ref	Expression
1		noel 3919	. 2 |- -. U. (/) e. (/)
2		bj-ismoored0 33061	. 2 |- ( (/) e. Moore_ -> U. (/) e. (/) )
3	1, 2	mto 188	1 |- -. (/) e. Moore_

Syntax hints:   -. wn 3   e. wcel 1990   (/)c0 3915   U.cuni 4436  Moore_cmoore 33057

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  ax-nul 4789

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-ral 2917  df-rex 2918  df-v 3202  df-dif 3577  df-in 3581  df-ss 3588  df-nul 3916  df-pw 4160  df-uni 4437  df-int 4476  df-bj-moore 33058

This theorem is referenced by:  bj-snmoore  33068