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Theorem 0cnd 7078
 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 7077 . 2 0 ∈ ℂ
21a1i 9 1 (𝜑 → 0 ∈ ℂ)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1409  ℂcc 6945  0cc0 6947 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-ext 2038  ax-1cn 7035  ax-icn 7037  ax-addcl 7038  ax-mulcl 7040  ax-i2m1 7047 This theorem depends on definitions:  df-bi 114  df-cleq 2049  df-clel 2052 This theorem is referenced by:  mulap0r  7680  mulap0  7709  diveqap0  7735  eqneg  7783  prodgt0  7893  un0addcl  8272  un0mulcl  8273  modsumfzodifsn  9346  iser0  9415  iser0f  9416  abs00ap  9889  abssubne0  9918  clim0c  10038
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