Theorem wleror 375

Description: Add disjunct to right of both sides

Hypothesis

Ref	Expression
wle.1	(a ≤2 b) = 1

Assertion

Ref	Expression
wleror	((a ∪ c) ≤2 (b ∪ c)) = 1

Proof of Theorem wleror

Step	Hyp	Ref	Expression
1		orordir 105	. . . . 5 ((a ∪ b) ∪ c) = ((a ∪ c) ∪ (b ∪ c))
2	1	bi1 110	. . . 4 (((a ∪ b) ∪ c) ≡ ((a ∪ c) ∪ (b ∪ c))) = 1
3	2	wr1 189	. . 3 (((a ∪ c) ∪ (b ∪ c)) ≡ ((a ∪ b) ∪ c)) = 1
4		wle.1	. . . . 5 (a ≤2 b) = 1
5	4	wdf-le2 361	. . . 4 ((a ∪ b) ≡ b) = 1
6	5	wr5-2v 348	. . 3 (((a ∪ b) ∪ c) ≡ (b ∪ c)) = 1
7	3, 6	wr2 353	. 2 (((a ∪ c) ∪ (b ∪ c)) ≡ (b ∪ c)) = 1
8	7	wdf-le1 360	1 ((a ∪ c) ≤2 (b ∪ c)) = 1

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

This theorem is referenced by:  wle2or 385

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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