ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  0cnd Unicode version

Theorem 0cnd 7001
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 7000 . 2  |-  0  e.  CC
21a1i 9 1  |-  ( ph  ->  0  e.  CC )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1393   CCcc 6868   0cc0 6870
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 6958  ax-icn 6960  ax-addcl 6961  ax-mulcl 6963  ax-i2m1 6970
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036
This theorem is referenced by:  mulap0r  7582  mulap0  7611  diveqap0  7637  eqneg  7684  prodgt0  7794  un0addcl  8187  un0mulcl  8188  iser0  9128  iser0f  9129  abs00ap  9538  abssubne0  9565  clim0c  9684
  Copyright terms: Public domain W3C validator