Theorem wdf-le1 378

Description: Define "less than or equal to" analogue for ≡ analogue of =. (Contributed by NM, 27-Sep-1997.)

Hypothesis

Ref	Expression
wdf-le1.1	((a ∪ b) ≡ b) = 1

Assertion

Ref	Expression
wdf-le1	(a ≤2 b) = 1

Proof of Theorem wdf-le1

Step	Hyp	Ref	Expression
1		df-le 129	. 2 (a ≤2 b) = ((a ∪ b) ≡ b)
2		wdf-le1.1	. 2 ((a ∪ b) ≡ b) = 1
3	1, 2	ax-r2 36	1 (a ≤2 b) = 1

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

This theorem was proved from axioms:  ax-r2 36

This theorem depends on definitions:  df-le 129

This theorem is referenced by:  wcomlem  382  wdf2le1  385  wlea  388  wle1  389  wleror  393  wbltr  397  wbile  401