Theorem u5lemnob 656

Description: Lemma for relevance implication study.

Assertion

Ref	Expression
u5lemnob	((a →5 b)⊥ ∪ b) = (a ∪ b)

Proof of Theorem u5lemnob

Step	Hyp	Ref	Expression
1		u5lemanb 601	. . 3 ((a →5 b) ∩ b⊥ ) = (a⊥ ∩ b⊥ )
2		anor1 80	. . 3 ((a →5 b) ∩ b⊥ ) = ((a →5 b)⊥ ∪ b)⊥
3		anor3 82	. . 3 (a⊥ ∩ b⊥ ) = (a ∪ b)⊥
4	1, 2, 3	3tr2 61	. 2 ((a →5 b)⊥ ∪ b)⊥ = (a ∪ b)⊥
5	4	con1 63	1 ((a →5 b)⊥ ∪ b) = (a ∪ b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₅ wi5 17

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-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i5 47  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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