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Theorem ceqsexvOLDOLD 3518
Description: Obsolete version of ceqsexv 3516 as of 12-Oct-2024. (Contributed by NM, 2-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ceqsexvOLD.1 𝐴 ∈ V
ceqsexvOLD.2 (𝑥 = 𝐴 → (𝜑𝜓))
Assertion
Ref Expression
ceqsexvOLDOLD (∃𝑥(𝑥 = 𝐴𝜑) ↔ 𝜓)
Distinct variable groups:   𝑥,𝐴   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem ceqsexvOLDOLD
StepHypRef Expression
1 nfv 1909 . 2 𝑥𝜓
2 ceqsexvOLD.1 . 2 𝐴 ∈ V
3 ceqsexvOLD.2 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
41, 2, 3ceqsex 3514 1 (∃𝑥(𝑥 = 𝐴𝜑) ↔ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wa 394   = wceq 1533  wex 1773  wcel 2098  Vcvv 3463
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-12 2166
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-ex 1774  df-nf 1778  df-clel 2802
This theorem is referenced by: (None)
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