Theorem bdne 9973

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 9940	. . 3 |- BOUNDED x = y
2	1	ax-bdn 9937	. 2 |- BOUNDED -. x = y
3		df-ne 2206	. 2 |- ( x =/= y <-> -. x = y )
4	2, 3	bd0r 9945	1 |- BOUNDED x =/= y

Syntax hints:   -. wn 3   =/= wne 2204  BOUNDED wbd 9932

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-bd0 9933  ax-bdn 9937  ax-bdeq 9940

This theorem depends on definitions:  df-bi 110  df-ne 2206

This theorem is referenced by: (None)