Theorem le0 147

Description: 0 is l.e. anything.

Assertion

Ref	Expression
le0	0 =< a

Proof of Theorem le0

Step	Hyp	Ref	Expression
1		ax-a2 31	. . 3 (0 v a) = (a v 0)
2		or0 102	. . 3 (a v 0) = a
3	1, 2	ax-r2 36	. 2 (0 v a) = a
4	3	df-le1 130	1 0 =< a

Syntax hints:   =< wle 2   v wo 6  0wf 9

This theorem is referenced by:  go1 343  ortha 438  ud4lem1a 577  mlalem 832  mh 879  gomaex4 900  oa3-6to3 987  oa64v 1030

This theorem was proved from axioms:  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-t 41  df-f 42  df-le1 130

Copyright terms: Public domain