Theorem negant 834

Description: Negated antecedent identity.

Hypothesis

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

Assertion

Ref	Expression
negant	(a_|_ ->1 c) = (b_|_ ->1 c)

Proof of Theorem negant

Step	Hyp	Ref	Expression
1		negant.1	. . 3 (a ->1 c) = (b ->1 c)
2	1	negantlem4 833	. 2 (a_|_ ->1 c) =< (b_|_ ->1 c)
3	1	ax-r1 34	. . 3 (b ->1 c) = (a ->1 c)
4	3	negantlem4 833	. 2 (b_|_ ->1 c) =< (a_|_ ->1 c)
5	2, 4	lebi 137	1 (a_|_ ->1 c) = (b_|_ ->1 c)

Syntax hints:   = wb 1  _|_wn 4   ->1 wi1 13

This theorem is referenced by:  negantlem6 836  negantlem10 843  elimcons 850

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-le1 122  df-le2 123  df-c1 124  df-c2 125

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