Theorem le0 139

Description: 0 is l.e. anything.

Assertion

Ref	Expression
le0	0 ≤ a

Proof of Theorem le0

Step	Hyp	Ref	Expression
1		ax-a2 30	. . 3 (0 ∪ a) = (a ∪ 0)
2		or0 94	. . 3 (a ∪ 0) = a
3	1, 2	ax-r2 35	. 2 (0 ∪ a) = a
4	3	df-le1 122	1 0 ≤ a

Syntax hints:   ≤ wle 2   ∪ wo 6  0wf 10

This theorem is referenced by:  go1 335  ortha 420  ud4lem1a 559  mlalem 814  mh 861  gomaex4 880  oa3-6to3 967  oa64v 1010

This theorem was proved from axioms:  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-t 40  df-f 41  df-le1 122

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