Theorem lem3.1 443

Description: Lemma used in proof of Thm. 3.1 of Pavicic 1993. (Contributed by NM, 12-Aug-1997.)

Hypotheses

Ref	Expression
lem3.1.1	(a ∪ b) = b
lem3.1.2	(b⊥ ∪ a) = 1

Assertion

Ref	Expression
lem3.1	a = b

Proof of Theorem lem3.1

Step	Hyp	Ref	Expression
1		lem3.1.1	. . . 4 (a ∪ b) = b
2		lem3.1.2	. . . 4 (b⊥ ∪ a) = 1
3	1, 2	wlem3.1 210	. . 3 (a ≡ b) = 1
4	3	ax-r1 35	. 2 1 = (a ≡ b)
5	4	r3a 440	1 a = b

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6  1wt 8

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  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41

This theorem is referenced by:  lem3a.1  444  oml  445  cmtr1com  493  i0cmtrcom  495  oaidlem2  931  oaidlem2g  932