Theorem oasr 926

Description: Reverse of oas 925 lemma for studying the orthoarguesian law. (Contributed by NM, 28-Dec-1998.)

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 778	. . 3 a⊥ ≤ (a →1 c)
2	1	leran 153	. 2 (a⊥ ∩ (a ∪ b)) ≤ ((a →1 c) ∩ (a ∪ b))
3		oasr.1	. 2 ((a →1 c) ∩ (a ∪ b)) ≤ c
4	2, 3	letr 137	1 (a⊥ ∩ (a ∪ b)) ≤ c

This proof depends on syntax axioms:   ≤ wle 2  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₁ wi1 12

This proof depends on axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This proof depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131

This theorem is used by: (None)