Theorem u1lem9b 778

Description: Lemma used in study of orthoarguesian law. Equation 4.11 of [MegPav2000] p. 23. This is the second part of the inequality. (Contributed by NM, 27-Dec-1998.)

Assertion

Ref	Expression
u1lem9b	a⊥ ≤ (a →1 b)

Proof of Theorem u1lem9b

Step	Hyp	Ref	Expression
1		leo 158	. 2 a⊥ ≤ (a⊥ ∪ (a ∩ b))
2		df-i1 44	. . 3 (a →1 b) = (a⊥ ∪ (a ∩ b))
3	2	ax-r1 35	. 2 (a⊥ ∪ (a ∩ b)) = (a →1 b)
4	1, 3	lbtr 139	1 a⊥ ≤ (a →1 b)

Syntax hints:   ≤ wle 2  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₁ wi1 12

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-i1 44  df-le1 130  df-le2 131

This theorem is referenced by:  u1lem9ab  779  kb10iii  893  oasr  926  axoa4  1034  lem4.6.3le2  1085