Theorem abf

Description: A class abstraction determined by a false formula is empty. (Contributed by NM, 20-Jan-2012) Avoid ax-8 , ax-10 , ax-11 , ax-12 . (Revised by Gino Giotto, 30-Jun-2024)

	Ref	Expression
Hypothesis	abf.1	|- -. ph
Assertion	abf	|- { x | ph } = (/)

Proof

Step	Hyp	Ref	Expression
1		abf.1	|- -. ph
2	1	bifal	|- ( ph <-> F. )
3	2	abbii	|- { x | ph } = { x | F. }
4		dfnul4	|- (/) = { x | F. }
5	3 4	eqtr4i	|- { x | ph } = (/)