Theorem 2vwomr2a 346

Description: 2-variable WOML rule.

Hypothesis

Ref	Expression
2vwomr2a.1	(a ->2 b) = 1

Assertion

Ref	Expression
2vwomr2a	(a ->1 b) = 1

Proof of Theorem 2vwomr2a

Step	Hyp	Ref	Expression
1		df-i1 43	. 2 (a ->1 b) = (a_|_ v (a ^ b))
2		df-i2 44	. . . . 5 (a ->2 b) = (b v (a_|_ ^ b_|_))
3	2	ax-r1 34	. . . 4 (b v (a_|_ ^ b_|_)) = (a ->2 b)
4		2vwomr2a.1	. . . 4 (a ->2 b) = 1
5	3, 4	ax-r2 35	. . 3 (b v (a_|_ ^ b_|_)) = 1
6	5	2vwomr2 344	. 2 (a_|_ v (a ^ b)) = 1
7	1, 6	ax-r2 35	1 (a ->1 b) = 1

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7  1wt 9   ->1 wi1 13   ->2 wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-wom 343

This theorem depends on definitions:  df-a 39  df-i1 43  df-i2 44

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