Theorem gomaex3h5 906

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

Hypotheses

Ref	Expression
gomaex3h5.11	r = ((p⊥ →1 q)⊥ ∩ (c ∪ d))
gomaex3h5.16	k = r
gomaex3h5.17	m = (p⊥ →1 q)

Assertion

Ref	Expression
gomaex3h5	k ≤ m⊥

Proof of Theorem gomaex3h5

Step	Hyp	Ref	Expression
1		gomaex3h5.11	. . 3 r = ((p⊥ →1 q)⊥ ∩ (c ∪ d))
2		lea 160	. . 3 ((p⊥ →1 q)⊥ ∩ (c ∪ d)) ≤ (p⊥ →1 q)⊥
3	1, 2	bltr 138	. 2 r ≤ (p⊥ →1 q)⊥
4		gomaex3h5.16	. 2 k = r
5		gomaex3h5.17	. . 3 m = (p⊥ →1 q)
6	5	ax-r4 37	. 2 m⊥ = (p⊥ →1 q)⊥
7	3, 4, 6	le3tr1 140	1 k ≤ m⊥

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₁ wi1 12

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