Theorem bdne 16879

Description: Inequality of two setvars is a bounded formula. (Contributed by BJ, 16-Oct-2019.)

Assertion

Ref	Expression
bdne	|- BOUNDED x =/= y

Proof of Theorem bdne

Step	Hyp	Ref	Expression
1		ax-bdeq 16846	. . 3 |- BOUNDED x = y
2	1	ax-bdn 16843	. 2 |- BOUNDED -. x = y
3		df-ne 2421	. 2 |- ( x =/= y <-> -. x = y )
4	2, 3	bd0r 16851	1 |- BOUNDED x =/= y

This proof depends on syntax axioms:   -. wn 3   =/= wne 2420  BOUNDED wbd 16838

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-bd0 16839  ax-bdn 16843  ax-bdeq 16846

This proof depends on definitions:  df-bi 117  df-ne 2421

This theorem is used by: (None)