Theorem u1lem9b 760

Description: Lemma used in study of orthoarguesian law.

Assertion

Ref	Expression
u1lem9b	a_|_ =< (a ->1 b)

Proof of Theorem u1lem9b

Step	Hyp	Ref	Expression
1		leo 150	. 2 a_|_ =< (a_|_ v (a ^ b))
2		df-i1 43	. . 3 (a ->1 b) = (a_|_ v (a ^ b))
3	2	ax-r1 34	. 2 (a_|_ v (a ^ b)) = (a ->1 b)
4	1, 3	lbtr 131	1 a_|_ =< (a ->1 b)

Syntax hints:   =< wle 2  _|_wn 4   v wo 6   ^ wa 7   ->1 wi1 13

This theorem is referenced by:  u1lem9ab 761  kb10iii 875  oasr 906  axoa4 1013

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

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

metamath.org