Theorem we0 5109

Description: Any relation is a well-ordering of the empty set. (Contributed by NM, 16-Mar-1997.)

Assertion

Ref	Expression
we0	|- R We (/)

Proof of Theorem we0

Step	Hyp	Ref	Expression
1		fr0 5093	. 2 |- R Fr (/)
2		so0 5068	. 2 |- R Or (/)
3		df-we 5075	. 2 |- ( R We (/) <-> ( R Fr (/) /\ R Or (/) ) )
4	1, 2, 3	mpbir2an 955	1 |- R We (/)

Syntax hints:   (/)c0 3915   Or wor 5034   Fr wfr 5070   We wwe 5072

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-ne 2795  df-ral 2917  df-rex 2918  df-rab 2921  df-v 3202  df-dif 3577  df-in 3581  df-ss 3588  df-nul 3916  df-po 5035  df-so 5036  df-fr 5073  df-we 5075

This theorem is referenced by:  ord0  5777  cantnf0  8572  cantnf  8590  wemapwe  8594  ltweuz  12760