Theorem gomaex3h4 885

Description: Hypothesis for Godowski 6-var -> Mayet Example 3.

Hypotheses

Ref	Expression
gomaex3h4.11	r = ((p⊥ →1 q)⊥ ∩ (c ∪ d))
gomaex3h4.15	j = (c ∪ d)⊥
gomaex3h4.16	k = r

Assertion

Ref	Expression
gomaex3h4	j ≤ k⊥

Proof of Theorem gomaex3h4

Step	Hyp	Ref	Expression
1		gomaex3h4.11	. . . 4 r = ((p⊥ →1 q)⊥ ∩ (c ∪ d))
2		lear 153	. . . 4 ((p⊥ →1 q)⊥ ∩ (c ∪ d)) ≤ (c ∪ d)
3	1, 2	bltr 130	. . 3 r ≤ (c ∪ d)
4	3	lecon 146	. 2 (c ∪ d)⊥ ≤ r⊥
5		gomaex3h4.15	. 2 j = (c ∪ d)⊥
6		gomaex3h4.16	. . 3 k = r
7	6	ax-r4 36	. 2 k⊥ = r⊥
8	4, 5, 7	le3tr1 132	1 j ≤ k⊥

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₁ wi1 13

This theorem is referenced by:  gomaex3lem5 898

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-le1 122  df-le2 123

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