Theorem ud4lem0a 254

Description: Introduce ->4 to the left.

Hypothesis

Ref	Expression
ud4lem0a.1	a = b

Assertion

Ref	Expression
ud4lem0a	(c ->4 a) = (c ->4 b)

Proof of Theorem ud4lem0a

Step	Hyp	Ref	Expression
1		ud4lem0a.1	. . . . 5 a = b
2	1	lan 70	. . . 4 (c ^ a) = (c ^ b)
3	1	lan 70	. . . 4 (c_|_ ^ a) = (c_|_ ^ b)
4	2, 3	2or 67	. . 3 ((c ^ a) v (c_|_ ^ a)) = ((c ^ b) v (c_|_ ^ b))
5	1	lor 66	. . . 4 (c_|_ v a) = (c_|_ v b)
6	1	ax-r4 36	. . . 4 a_|_ = b_|_
7	5, 6	2an 72	. . 3 ((c_|_ v a) ^ a_|_) = ((c_|_ v b) ^ b_|_)
8	4, 7	2or 67	. 2 (((c ^ a) v (c_|_ ^ a)) v ((c_|_ v a) ^ a_|_)) = (((c ^ b) v (c_|_ ^ b)) v ((c_|_ v b) ^ b_|_))
9		df-i4 46	. 2 (c ->4 a) = (((c ^ a) v (c_|_ ^ a)) v ((c_|_ v a) ^ a_|_))
10		df-i4 46	. 2 (c ->4 b) = (((c ^ b) v (c_|_ ^ b)) v ((c_|_ v b) ^ b_|_))
11	8, 9, 10	3tr1 60	1 (c ->4 a) = (c ->4 b)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->4 wi4 16

This theorem is referenced by:  i4i3 263  nom43 320  ud4 580

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-i4 46

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