Theorem or42 85

Description: Rearrange disjuncts. (Contributed by NM, 4-Mar-2006.)

Assertion

Ref	Expression
or42	((a ∪ b) ∪ (c ∪ d)) = ((a ∪ d) ∪ (b ∪ c))

Proof of Theorem or42

Step	Hyp	Ref	Expression
1		ax-a2 31	. . 3 (c ∪ d) = (d ∪ c)
2	1	lor 70	. 2 ((a ∪ b) ∪ (c ∪ d)) = ((a ∪ b) ∪ (d ∪ c))
3		or4 84	. 2 ((a ∪ b) ∪ (d ∪ c)) = ((a ∪ d) ∪ (b ∪ c))
4	2, 3	ax-r2 36	1 ((a ∪ b) ∪ (c ∪ d)) = ((a ∪ d) ∪ (b ∪ c))

This proof depends on syntax axioms:   = wb 1   ∪ wo 6

This proof depends on axioms:  ax-a2 31  ax-a3 32  ax-r1 35  ax-r2 36  ax-r5 38

This theorem is used by:  wdcom  1105