Theorem bj-abf 32903

Description: Shorter proof of abf 3978 (which should be kept as abfALT). (Contributed by BJ, 24-Jul-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-abf.1	|- -. ph

Assertion

Ref	Expression
bj-abf	|- { x | ph } = (/)

Proof of Theorem bj-abf

Step	Hyp	Ref	Expression
1		bj-ab0 32902	. 2 |- ( A. x -. ph -> { x | ph } = (/) )
2		bj-abf.1	. 2 |- -. ph
3	1, 2	mpg 1724	1 |- { x | ph } = (/)

Syntax hints:   -. wn 3   = wceq 1483   {cab 2608   (/)c0 3915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-nul 3916

This theorem is referenced by: (None)