Theorem ud5lem0a 256

Description: Introduce ->5 to the left.

Hypothesis

Ref	Expression
ud5lem0a.1	a = b

Assertion

Ref	Expression
ud5lem0a	(c ->5 a) = (c ->5 b)

Proof of Theorem ud5lem0a

Step	Hyp	Ref	Expression
1		ud5lem0a.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	ax-r4 36	. . . 4 a_|_ = b_|_
6	5	lan 70	. . 3 (c_|_ ^ a_|_) = (c_|_ ^ b_|_)
7	4, 6	2or 67	. 2 (((c ^ a) v (c_|_ ^ a)) v (c_|_ ^ a_|_)) = (((c ^ b) v (c_|_ ^ b)) v (c_|_ ^ b_|_))
8		df-i5 47	. 2 (c ->5 a) = (((c ^ a) v (c_|_ ^ a)) v (c_|_ ^ a_|_))
9		df-i5 47	. 2 (c ->5 b) = (((c ^ b) v (c_|_ ^ b)) v (c_|_ ^ b_|_))
10	7, 8, 9	3tr1 60	1 (c ->5 a) = (c ->5 b)

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->5 wi5 17

This theorem is referenced by:  nom45 322  ud5 581

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-i5 47

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