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Theorem bj-n0i 31969
Description: Inference associated with n0 3793. (Minimizes three statements by a total of 29 bytes.) (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 3793 . 2 (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥𝐴)
31, 2mpbi 218 1 𝑥 𝑥𝐴
Colors of variables: wff setvar class
Syntax hints:  wex 1694  wcel 1938  wne 2684  c0 3777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-11 1971  ax-12 1983  ax-13 2137  ax-ext 2494
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1699  df-sb 1831  df-clab 2501  df-cleq 2507  df-clel 2510  df-nfc 2644  df-ne 2686  df-v 3079  df-dif 3447  df-nul 3778
This theorem is referenced by: (None)
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