Theorem gomaex3h11 892

Description: Hypothesis for Godowski 6-var -> Mayet Example 3.

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 151	. . 3 f ≤ (e ∪ f)
2	1	lecon 146	. 2 (e ∪ f)⊥ ≤ f⊥
3		gomaex3h11.22	. 2 y = (e ∪ f)⊥
4		gomaex3h11.23	. . 3 z = f
5	4	ax-r4 36	. 2 z⊥ = f⊥
6	2, 3, 5	le3tr1 132	1 y ≤ z⊥

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

This theorem is referenced by:  gomaex3lem5 898

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-le1 122  df-le2 123

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