Theorem gomaex3h3 904

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

Hypotheses

Ref	Expression
gomaex3h3.14	i = c
gomaex3h3.15	j = (c ∪ d)⊥

Assertion

Ref	Expression
gomaex3h3	i ≤ j⊥

Proof of Theorem gomaex3h3

Step	Hyp	Ref	Expression
1		leo 158	. . 3 c ≤ (c ∪ d)
2		ax-a1 30	. . 3 (c ∪ d) = (c ∪ d)⊥ ⊥
3	1, 2	lbtr 139	. 2 c ≤ (c ∪ d)⊥ ⊥
4		gomaex3h3.14	. 2 i = c
5		gomaex3h3.15	. . 3 j = (c ∪ d)⊥
6	5	ax-r4 37	. 2 j⊥ = (c ∪ d)⊥ ⊥
7	3, 4, 6	le3tr1 140	1 i ≤ j⊥

Syntax hints:   = wb 1   ≤ wle 2  ^⊥ wn 4   ∪ wo 6

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