Theorem ud2lem0b 259

Description: Introduce ->2 to the right.

Hypothesis

Ref	Expression
ud2lem0a.1	a = b

Assertion

Ref	Expression
ud2lem0b	(a ->2 c) = (b ->2 c)

Proof of Theorem ud2lem0b

Step	Hyp	Ref	Expression
1		ud2lem0a.1	. . . . 5 a = b
2	1	ax-r4 37	. . . 4 a' = b'
3	2	ran 78	. . 3 (a' ^ c') = (b' ^ c')
4	3	lor 70	. 2 (c v (a' ^ c')) = (c v (b' ^ c'))
5		df-i2 45	. 2 (a ->2 c) = (c v (a' ^ c'))
6		df-i2 45	. 2 (b ->2 c) = (c v (b' ^ c'))
7	4, 5, 6	3tr1 63	1 (a ->2 c) = (b ->2 c)

Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13

This theorem is referenced by:  i2i1 267  i1i2con1 268  ud2 596  2oath1i1 827

This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-i2 45

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