Theorem qlhoml1b 136

Description: An ortholattice inequality, corresponding to a theorem provable in Hilbert space.

Assertion

Ref	Expression
qlhoml1b	a_|__|_ =< a

Proof of Theorem qlhoml1b

Step	Hyp	Ref	Expression
1		ax-a1 29	. . 3 a = a_|__|_
2	1	ax-r1 34	. 2 a_|__|_ = a
3	2	bile 134	1 a_|__|_ =< a

Syntax hints:   =< wle 2  _|_wn 4

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-t 40  df-f 41  df-le1 122

metamath.org