Theorem gomaex3h11 912

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

Hypotheses

Ref	Expression
gomaex3h11.22	y = (e ∪ f)⊥
gomaex3h11.23	z = f

Assertion

Ref	Expression
gomaex3h11	y ≤ z⊥

Proof of Theorem gomaex3h11

Step	Hyp	Ref	Expression
1		leor 159	. . 3 f ≤ (e ∪ f)
2	1	lecon 154	. 2 (e ∪ f)⊥ ≤ f⊥
3		gomaex3h11.22	. 2 y = (e ∪ f)⊥
4		gomaex3h11.23	. . 3 z = f
5	4	ax-r4 37	. 2 z⊥ = f⊥
6	2, 3, 5	le3tr1 140	1 y ≤ z⊥

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ wo 6

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