Theorem nom32 313

Description: Part of Lemma 3.3(14) from "Non-Orthomodular Models..." paper.

Assertion

Ref	Expression
nom32	((a ^ b) ==2 a) = (a ->1 b)

Proof of Theorem nom32

Step	Hyp	Ref	Expression
1		nomb32 292	. . 3 (a ==3 (a ^ b)) = ((a ^ b) ==2 a)
2	1	ax-r1 34	. 2 ((a ^ b) ==2 a) = (a ==3 (a ^ b))
3		nom23 308	. 2 (a ==3 (a ^ b)) = (a ->1 b)
4	2, 3	ax-r2 35	1 ((a ^ b) ==2 a) = (a ->1 b)

Syntax hints:   = wb 1   ^ wa 7   ->1 wi1 13   ==2 wid2 20   ==3 wid3 21

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

This theorem depends on definitions:  df-a 39  df-t 40  df-i1 43  df-id2 50  df-id3 51  df-le1 122  df-le2 123

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