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Theorem spcegvOLD 3573
 Description: Obsolete version of spcegv 3572 as of 25-Aug-2023. (Contributed by NM, 14-Aug-1994.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
spcgv.1 (𝑥 = 𝐴 → (𝜑𝜓))
Assertion
Ref Expression
spcegvOLD (𝐴𝑉 → (𝜓 → ∃𝑥𝜑))
Distinct variable groups:   𝜓,𝑥   𝑥,𝐴
Allowed substitution hints:   𝜑(𝑥)   𝑉(𝑥)

Proof of Theorem spcegvOLD
StepHypRef Expression
1 nfcv 2979 . 2 𝑥𝐴
2 nfv 1915 . 2 𝑥𝜓
3 spcgv.1 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
41, 2, 3spcegf 3566 1 (𝐴𝑉 → (𝜓 → ∃𝑥𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   = wceq 1538  ∃wex 1781   ∈ wcel 2114 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-v 3471 This theorem is referenced by: (None)
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