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Theorem 0cnd 7174
Description: 0 is a complex number, deductive form. (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
0cnd  |-  ( ph  ->  0  e.  CC )

Proof of Theorem 0cnd
StepHypRef Expression
1 0cn 7173 . 2  |-  0  e.  CC
21a1i 9 1  |-  ( ph  ->  0  e.  CC )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   CCcc 7041   0cc0 7043
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-1cn 7131  ax-icn 7133  ax-addcl 7134  ax-mulcl 7136  ax-i2m1 7143
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-clel 2078
This theorem is referenced by:  mulap0r  7782  mulap0  7811  diveqap0  7837  eqneg  7887  prodgt0  7997  un0addcl  8388  un0mulcl  8389  modsumfzodifsn  9478  iser0  9568  iser0f  9569  abs00ap  10086  abssubne0  10115  clim0c  10263  isumrblem  10337
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