Theorem gomaex3h2 903

Description: Hypothesis for Godowski 6-var -> Mayet Example 3. (Contributed by NM, 29-Nov-1999.)

Hypotheses

Ref	Expression
gomaex3h2.2	b ≤ c⊥
gomaex3h2.13	h = b
gomaex3h2.14	i = c

Assertion

Ref	Expression
gomaex3h2	h ≤ i⊥

Proof of Theorem gomaex3h2

Step	Hyp	Ref	Expression
1		gomaex3h2.2	. 2 b ≤ c⊥
2		gomaex3h2.13	. 2 h = b
3		gomaex3h2.14	. . 3 i = c
4	3	ax-r4 37	. 2 i⊥ = c⊥
5	1, 2, 4	le3tr1 140	1 h ≤ i⊥

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4

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-le1 130  df-le2 131

This theorem is referenced by:  gomaex3lem5  918