Theorem lem3a.1 426

Description: Lemma used in proof of Th. 3.1 of Pavicic 1993.

Hypotheses

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

Assertion

Ref	Expression
lem3a.1	(a ∪ b) = a

Proof of Theorem lem3a.1

Step	Hyp	Ref	Expression
1		lem3.1.1	. . . . 5 (a ∪ b) = b
2		lem3.1.2	. . . . 5 (b⊥ ∪ a) = 1
3	1, 2	lem3.1 425	. . . 4 a = b
4	3	ax-r1 34	. . 3 b = a
5	4	lor 66	. 2 (a ∪ b) = (a ∪ a)
6		oridm 102	. 2 (a ∪ a) = a
7	5, 6	ax-r2 35	1 (a ∪ b) = a

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6  1wt 9

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  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41

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