Theorem negant5 845

Description: Negated antecedent identity.

Hypothesis

Ref	Expression
negant.1	(a ->1 c) = (b ->1 c)

Assertion

Ref	Expression
negant5	(a_|_ ->5 c) = (b_|_ ->5 c)

Proof of Theorem negant5

Step	Hyp	Ref	Expression
1		negant.1	. . . 4 (a ->1 c) = (b ->1 c)
2	1	negant2 840	. . 3 (a_|_ ->2 c) = (b_|_ ->2 c)
3	1	negant4 844	. . 3 (a_|_ ->4 c) = (b_|_ ->4 c)
4	2, 3	2an 72	. 2 ((a_|_ ->2 c) ^ (a_|_ ->4 c)) = ((b_|_ ->2 c) ^ (b_|_ ->4 c))
5		u24lem 752	. 2 ((a_|_ ->2 c) ^ (a_|_ ->4 c)) = (a_|_ ->5 c)
6		u24lem 752	. 2 ((b_|_ ->2 c) ^ (b_|_ ->4 c)) = (b_|_ ->5 c)
7	4, 5, 6	3tr2 61	1 (a_|_ ->5 c) = (b_|_ ->5 c)

Syntax hints:   = wb 1  _|_wn 4   ^ wa 7   ->1 wi1 13   ->2 wi2 14   ->4 wi4 16   ->5 wi5 17

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i1 43  df-i2 44  df-i3 45  df-i4 46  df-i5 47  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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