Theorem ud1lem0b 256

Description: Introduce ->1 to the right.

Hypothesis

Ref	Expression
ud1lem0a.1	a = b

Assertion

Ref	Expression
ud1lem0b	(a ->1 c) = (b ->1 c)

Proof of Theorem ud1lem0b

Step	Hyp	Ref	Expression
1		ud1lem0a.1	. . . 4 a = b
2	1	ax-r4 37	. . 3 a' = b'
3	1	ran 78	. . 3 (a ^ c) = (b ^ c)
4	2, 3	2or 72	. 2 (a' v (a ^ c)) = (b' v (b ^ c))
5		df-i1 44	. 2 (a ->1 c) = (a' v (a ^ c))
6		df-i1 44	. 2 (b ->1 c) = (b' v (b ^ c))
7	4, 5, 6	3tr1 63	1 (a ->1 c) = (b ->1 c)

Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12

This theorem is referenced by:  ud1lem0ab 257  wql1 293  ud1 595  oi3oa3lem1 732  oi3oa3 733  u1lem12 781  1oaiii 823  sac 835  oa4to4u 973  oa4uto4g 975  oa4gto4u 976

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-i1 44

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