Theorem i3lem2 487

Description: Lemma for Kalmbach implication.

Hypothesis

Ref	Expression
i3lem.1	(a →3 b) = 1

Assertion

Ref	Expression
i3lem2	a C b

Proof of Theorem i3lem2

Step	Hyp	Ref	Expression
1		i3lem.1	. . . . . 6 (a →3 b) = 1
2	1	i3lem1 486	. . . . 5 ((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ )) = a⊥
3	2	ax-r1 34	. . . 4 a⊥ = ((a⊥ ∩ b) ∪ (a⊥ ∩ b⊥ ))
4	3	df-c1 124	. . 3 a⊥ C b
5	4	comcom2 175	. 2 a⊥ C b⊥
6	5	comcom5 440	1 a C b

Syntax hints:   = wb 1   C wc 3  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 9   →₃ wi3 15

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i3 45  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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