Theorem gomaex3h12 913

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

Hypotheses

Ref	Expression
gomaex3h12.6	f ≤ a⊥
gomaex3h12.12	g = a
gomaex3h12.23	z = f

Assertion

Ref	Expression
gomaex3h12	z ≤ g⊥

Proof of Theorem gomaex3h12

Step	Hyp	Ref	Expression
1		gomaex3h12.6	. 2 f ≤ a⊥
2		gomaex3h12.23	. 2 z = f
3		gomaex3h12.12	. . 3 g = a
4	3	ax-r4 37	. 2 g⊥ = a⊥
5	1, 2, 4	le3tr1 140	1 z ≤ g⊥

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