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Theorem vtoclfOLD 3519
Description: Obsolete version of vtoclf 3518 as of 26-Jan-2025. (Contributed by NM, 30-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
vtoclf.1 𝑥𝜓
vtoclf.2 𝐴 ∈ V
vtoclf.3 (𝑥 = 𝐴 → (𝜑𝜓))
vtoclf.4 𝜑
Assertion
Ref Expression
vtoclfOLD 𝜓
Distinct variable group:   𝑥,𝐴
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥)

Proof of Theorem vtoclfOLD
StepHypRef Expression
1 vtoclf.1 . . 3 𝑥𝜓
2 vtoclf.2 . . . . 5 𝐴 ∈ V
32isseti 3462 . . . 4 𝑥 𝑥 = 𝐴
4 vtoclf.3 . . . . 5 (𝑥 = 𝐴 → (𝜑𝜓))
54biimpd 228 . . . 4 (𝑥 = 𝐴 → (𝜑𝜓))
63, 5eximii 1840 . . 3 𝑥(𝜑𝜓)
71, 619.36i 2225 . 2 (∀𝑥𝜑𝜓)
8 vtoclf.4 . 2 𝜑
97, 8mpg 1800 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1542  wnf 1786  wcel 2107  Vcvv 3447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-12 2172
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-nf 1787  df-clel 2811
This theorem is referenced by: (None)
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