Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-n0i Structured version   Visualization version   GIF version

Theorem bj-n0i 33260
 Description: Inference associated with n0 4074. Shortens 2ndcdisj 21481 (2888>2878), notzfaus 4989 (264>253). (Contributed by BJ, 22-Apr-2019.)
Hypothesis
Ref Expression
bj-n0i.1 𝐴 ≠ ∅
Assertion
Ref Expression
bj-n0i 𝑥 𝑥𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-n0i
StepHypRef Expression
1 bj-n0i.1 . 2 𝐴 ≠ ∅
2 n0 4074 . 2 (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥𝐴)
31, 2mpbi 220 1 𝑥 𝑥𝐴
 Colors of variables: wff setvar class Syntax hints:  ∃wex 1853   ∈ wcel 2139   ≠ wne 2932  ∅c0 4058 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ne 2933  df-v 3342  df-dif 3718  df-nul 4059 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator