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Theorem 0zd 8255
Description: Zero is an integer, deductive form (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
0zd (𝜑 → 0 ∈ ℤ)

Proof of Theorem 0zd
StepHypRef Expression
1 0z 8254 . 2 0 ∈ ℤ
21a1i 9 1 (𝜑 → 0 ∈ ℤ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1393  0cc0 6887  cz 8243
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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-1re 6976  ax-addrcl 6979  ax-rnegex 6991
This theorem depends on definitions:  df-bi 110  df-3or 886  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-rab 2315  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-neg 7183  df-z 8244
This theorem is referenced by:  fzctr  8989  fzosubel3  9050  frecfzennn  9177  frechashgf1o  9179  exp0  9233  fzomaxdiflem  9682  nn0seqcvgd  9853  ialginv  9859  ialgcvg  9860  ialgcvga  9863  ialgfx  9864
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