Theorem bj-abf 34228

Description: Shorter proof of abf 4356 (which should be kept as abfALT). (Contributed by BJ, 24-Jul-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-abf.1	⊢ ¬ 𝜑

Assertion

Ref	Expression
bj-abf	⊢ {𝑥 ∣ 𝜑} = ∅

Proof of Theorem bj-abf

Step	Hyp	Ref	Expression
1		bj-ab0 34227	. 2 ⊢ (∀𝑥 ¬ 𝜑 → {𝑥 ∣ 𝜑} = ∅)
2		bj-abf.1	. 2 ⊢ ¬ 𝜑
3	1, 2	mpg 1798	1 ⊢ {𝑥 ∣ 𝜑} = ∅

Syntax hints:  ¬ wn 3   = wceq 1537  {cab 2799  ∅c0 4291

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-dif 3939  df-nul 4292

This theorem is referenced by: (None)