Theorem wdf-le2 379

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

Hypothesis

Ref	Expression
wdf-le2.1	(a ≤2 b) = 1

Assertion

Ref	Expression
wdf-le2	((a ∪ b) ≡ b) = 1

Proof of Theorem wdf-le2

Step	Hyp	Ref	Expression
1		df-le 129	. . 3 (a ≤2 b) = ((a ∪ b) ≡ b)
2	1	ax-r1 35	. 2 ((a ∪ b) ≡ b) = (a ≤2 b)
3		wdf-le2.1	. 2 (a ≤2 b) = 1
4	2, 3	ax-r2 36	1 ((a ∪ b) ≡ b) = 1

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

This theorem was proved from axioms:  ax-r1 35  ax-r2 36

This theorem depends on definitions:  df-le 129

This theorem is referenced by:  wom4  380  wdf2le2  386  wleror  393  wlecon  395  wletr  396  wbltr  397  wlebi  402