Theorem oasr 906

Description: Reverse of oas 905 lemma for studying the orthoarguesian law.

Hypothesis

Ref	Expression
oasr.1	((a →1 c) ∩ (a ∪ b)) ≤ c

Assertion

Ref	Expression
oasr	(a⊥ ∩ (a ∪ b)) ≤ c

Proof of Theorem oasr

Step	Hyp	Ref	Expression
1		u1lem9b 760	. . 3 a⊥ ≤ (a →1 c)
2	1	leran 145	. 2 (a⊥ ∩ (a ∪ b)) ≤ ((a →1 c) ∩ (a ∪ b))
3		oasr.1	. 2 ((a →1 c) ∩ (a ∪ b)) ≤ c
4	2, 3	letr 129	1 (a⊥ ∩ (a ∪ b)) ≤ c

Syntax hints:   ≤ wle 2  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₁ wi1 13

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

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-i1 43  df-le1 122  df-le2 123

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