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Theorem 0cnd 7018
Description: 0 is a complex number, deductive form. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
0cnd (𝜑 → 0 ∈ ℂ)

Proof of Theorem 0cnd
StepHypRef Expression
1 0cn 7017 . 2 0 ∈ ℂ
21a1i 9 1 (𝜑 → 0 ∈ ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1393  cc 6885  0cc0 6887
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-1cn 6975  ax-icn 6977  ax-addcl 6978  ax-mulcl 6980  ax-i2m1 6987
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036
This theorem is referenced by:  mulap0r  7604  mulap0  7633  diveqap0  7659  eqneg  7706  prodgt0  7816  un0addcl  8213  un0mulcl  8214  iser0  9224  iser0f  9225  abs00ap  9634  abssubne0  9661  clim0c  9780
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