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Theorem bj-vtoclf 32883
Description: Remove dependency on ax-ext 2600, df-clab 2607 and df-cleq 2613 (and df-sb 1879 and df-v 3197) from vtoclf 3253. (Contributed by BJ, 6-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-vtoclf.nf 𝑥𝜓
bj-vtoclf.s 𝐴𝑉
bj-vtoclf.maj (𝑥 = 𝐴 → (𝜑𝜓))
bj-vtoclf.min 𝜑
Assertion
Ref Expression
bj-vtoclf 𝜓
Distinct variable groups:   𝑥,𝐴   𝑥,𝑉
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥)

Proof of Theorem bj-vtoclf
StepHypRef Expression
1 bj-vtoclf.nf . . 3 𝑥𝜓
2 bj-vtoclf.s . . . . 5 𝐴𝑉
32bj-issetiv 32838 . . . 4 𝑥 𝑥 = 𝐴
4 bj-vtoclf.maj . . . . 5 (𝑥 = 𝐴 → (𝜑𝜓))
54biimpd 219 . . . 4 (𝑥 = 𝐴 → (𝜑𝜓))
63, 5eximii 1762 . . 3 𝑥(𝜑𝜓)
71, 619.36i 2097 . 2 (∀𝑥𝜑𝜓)
8 bj-vtoclf.min . 2 𝜑
97, 8mpg 1722 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1481  wnf 1706  wcel 1988
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-12 2045
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1703  df-nf 1708  df-clel 2616
This theorem is referenced by:  bj-vtocl  32884
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