Theorem bdne 15583

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 15550	. . 3 |- BOUNDED x = y
2	1	ax-bdn 15547	. 2 |- BOUNDED -. x = y
3		df-ne 2368	. 2 |- ( x =/= y <-> -. x = y )
4	2, 3	bd0r 15555	1 |- BOUNDED x =/= y

Syntax hints:   -. wn 3   =/= wne 2367  BOUNDED wbd 15542

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-bd0 15543  ax-bdn 15547  ax-bdeq 15550

This theorem depends on definitions:  df-bi 117  df-ne 2368

This theorem is referenced by: (None)