Theorem wbile 383

Description: Biconditional to l.e.

Hypothesis

Ref	Expression
wbile.1	(a ≡ b) = 1

Assertion

Ref	Expression
wbile	(a ≤2 b) = 1

Proof of Theorem wbile

Step	Hyp	Ref	Expression
1		wbile.1	. . . 4 (a ≡ b) = 1
2	1	wr5-2v 348	. . 3 ((a ∪ b) ≡ (b ∪ b)) = 1
3		oridm 102	. . . 4 (b ∪ b) = b
4	3	bi1 110	. . 3 ((b ∪ b) ≡ b) = 1
5	2, 4	wr2 353	. 2 ((a ∪ b) ≡ b) = 1
6	5	wdf-le1 360	1 (a ≤2 b) = 1

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

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-wom 343

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-le 121  df-le1 122  df-le2 123

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