Theorem wdf-le1 360

Description: Define 'less than or equal to' analogue for ≡ analogue of =.

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 121	. 2 (a ≤2 b) = ((a ∪ b) ≡ b)
2		wdf-le1.1	. 2 ((a ∪ b) ≡ b) = 1
3	1, 2	ax-r2 35	1 (a ≤2 b) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∪ wo 6  1wt 9   ≤₂ wle2 11

This theorem is referenced by:  wcomlem 364  wdf2le1 367  wlea 370  wle1 371  wleror 375  wbltr 379  wbile 383

This theorem was proved from axioms:  ax-r2 35

This theorem depends on definitions:  df-le 121

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