Theorem gomaex3h9 910

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

Hypotheses

Ref	Expression
gomaex3h9.20	w = q⊥
gomaex3h9.21	x = q

Assertion

Ref	Expression
gomaex3h9	w ≤ x⊥

Proof of Theorem gomaex3h9

Step	Hyp	Ref	Expression
1		leid 148	. 2 q⊥ ≤ q⊥
2		gomaex3h9.20	. 2 w = q⊥
3		gomaex3h9.21	. . 3 x = q
4	3	ax-r4 37	. 2 x⊥ = q⊥
5	1, 2, 4	le3tr1 140	1 w ≤ x⊥

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-t 41  df-f 42  df-le1 130  df-le2 131

This theorem is referenced by:  gomaex3lem5  918