Theorem lem3.3.5lem 1054

Description: A fundamental property in quantum logic. Lemma for lem3.3.5 1055. (Contributed by Roy F. Longton, 28-Jun-2005.) (Revised by Roy F. Longton, 3-Jul-2005.)

Hypothesis

Ref	Expression
lem3.3.5lem.1	1 ≤ a

Assertion

Ref	Expression
lem3.3.5lem	a = 1

Proof of Theorem lem3.3.5lem

Step	Hyp	Ref	Expression
1		le1 146	. 2 a ≤ 1
2		lem3.3.5lem.1	. 2 1 ≤ a
3	1, 2	lebi 145	1 a = 1

Syntax hints:   = wb 1   ≤ wle 2  1wt 8

This theorem was proved from axioms:  ax-a2 31  ax-a4 33  ax-r1 35  ax-r2 36  ax-r5 38

This theorem depends on definitions:  df-t 41  df-le1 130  df-le2 131

This theorem is referenced by:  lem3.3.5  1055  lem3.4.3  1076  lem4.6.6i1j3  1094