Theorem wle0 390

Description: 0 is less than or equal to anything. (Contributed by NM, 11-Oct-1997.)

Assertion

Ref	Expression
wle0	(0 ≤2 a) = 1

Proof of Theorem wle0

Step	Hyp	Ref	Expression
1		df-le 129	. 2 (0 ≤2 a) = ((0 ∪ a) ≡ a)
2		ax-a2 31	. . . 4 (0 ∪ a) = (a ∪ 0)
3		or0 102	. . . 4 (a ∪ 0) = a
4	2, 3	ax-r2 36	. . 3 (0 ∪ a) = a
5	4	bi1 118	. 2 ((0 ∪ a) ≡ a) = 1
6	1, 5	ax-r2 36	1 (0 ≤2 a) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∪ wo 6  1wt 8  0wf 9   ≤₂ wle2 10

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le 129

This theorem is referenced by: (None)