Theorem ud1lem0a 247

Description: Introduce ->1 to the left.

Hypothesis

Ref	Expression
ud1lem0a.1	a = b

Assertion

Ref	Expression
ud1lem0a	(c ->1 a) = (c ->1 b)

Proof of Theorem ud1lem0a

Step	Hyp	Ref	Expression
1		ud1lem0a.1	. . . 4 a = b
2	1	lan 70	. . 3 (c ^ a) = (c ^ b)
3	2	lor 66	. 2 (c_|_ v (c ^ a)) = (c_|_ v (c ^ b))
4		df-i1 43	. 2 (c ->1 a) = (c_|_ v (c ^ a))
5		df-i1 43	. 2 (c ->1 b) = (c_|_ v (c ^ b))
6	3, 4, 5	3tr1 60	1 (c ->1 a) = (c ->1 b)

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

This theorem is referenced by:  ud1lem0ab 249  wql1 285  nom42 319  ud1 577  u3lem13b 772  2oai1u 804  1oaiii 805  oa3to4lem1 925  oa3to4lem2 926  oa4to6lem1 940  oa4to6lem2 941  oa4to6lem3 942

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

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

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