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Theorem c0exALT 39017
Description: Alternate proof of c0ex 10624 using more set theory axioms but fewer complex number axioms (add ax-10 2138, ax-11 2153, ax-13 2385, ax-nul 5207, and remove ax-1cn 10584, ax-icn 10585, ax-addcl 10586, and ax-mulcl 10588). (Contributed by Steven Nguyen, 4-Dec-2022.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
c0exALT 0 ∈ V

Proof of Theorem c0exALT
StepHypRef Expression
1 ax-i2m1 10594 . . 3 ((i · i) + 1) = 0
21eqcomi 2835 . 2 0 = ((i · i) + 1)
32ovexi 7182 1 0 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  Vcvv 3500  (class class class)co 7148  0cc0 10526  1c1 10527  ici 10528   + caddc 10529   · cmul 10531
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798  ax-nul 5207  ax-i2m1 10594
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-mo 2620  df-eu 2652  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-rex 3149  df-v 3502  df-sbc 3777  df-dif 3943  df-un 3945  df-in 3947  df-ss 3956  df-nul 4296  df-sn 4565  df-pr 4567  df-uni 4838  df-iota 6312  df-fv 6360  df-ov 7151
This theorem is referenced by: (None)
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