Theorem gomaex3h8 909

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

Hypotheses

Ref	Expression
gomaex3h8.19	u = (p⊥ ∩ q)
gomaex3h8.20	w = q⊥

Assertion

Ref	Expression
gomaex3h8	u ≤ w⊥

Proof of Theorem gomaex3h8

Step	Hyp	Ref	Expression
1		lear 161	. . 3 (p⊥ ∩ q) ≤ q
2		ax-a1 30	. . 3 q = q⊥ ⊥
3	1, 2	lbtr 139	. 2 (p⊥ ∩ q) ≤ q⊥ ⊥
4		gomaex3h8.19	. 2 u = (p⊥ ∩ q)
5		gomaex3h8.20	. . 3 w = q⊥
6	5	ax-r4 37	. 2 w⊥ = q⊥ ⊥
7	3, 4, 6	le3tr1 140	1 u ≤ w⊥

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∩ wa 7

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