Theorem le0 147

Description: 0 is less than or equal to anything. (Contributed by NM, 30-Aug-1997.)

Assertion

Ref	Expression
le0	0 ≤ a

Proof of Theorem le0

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

Syntax hints:   ≤ wle 2   ∪ wo 6  0wf 9

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

This theorem is referenced by:  go1  343  ortha  438  ud4lem1a  577  mlalem  832  mh  879  gomaex4  900  oa3-6to3  987  oa64v  1031  vneulem7  1137  vneulemexp  1148