Theorem gomaex3h6 907

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

Hypotheses

Ref	Expression
gomaex3h6.17	m = (p⊥ →1 q)
gomaex3h6.18	n = (p⊥ →1 q)⊥

Assertion

Ref	Expression
gomaex3h6	m ≤ n⊥

Proof of Theorem gomaex3h6

Step	Hyp	Ref	Expression
1		leid 148	. . 3 (p⊥ →1 q) ≤ (p⊥ →1 q)
2		ax-a1 30	. . 3 (p⊥ →1 q) = (p⊥ →1 q)⊥ ⊥
3	1, 2	lbtr 139	. 2 (p⊥ →1 q) ≤ (p⊥ →1 q)⊥ ⊥
4		gomaex3h6.17	. 2 m = (p⊥ →1 q)
5		gomaex3h6.18	. . 3 n = (p⊥ →1 q)⊥
6	5	ax-r4 37	. 2 n⊥ = (p⊥ →1 q)⊥ ⊥
7	3, 4, 6	le3tr1 140	1 m ≤ n⊥

This proof depends on syntax axioms:   = wb 1   ≤ wle 2  ^⊥ wn 4   →₁ wi1 12

This proof depends on axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This proof depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131

This theorem is used by:  gomaex3lem5  918