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Theorem bj-vtoclf 33431
 Description: Remove dependency on ax-ext 2804, df-clab 2813 and df-cleq 2819 (and df-sb 2070 and df-v 3417) from vtoclf 3475. (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 33384 . . . 4 𝑥 𝑥 = 𝐴
4 bj-vtoclf.maj . . . . 5 (𝑥 = 𝐴 → (𝜑𝜓))
54biimpd 221 . . . 4 (𝑥 = 𝐴 → (𝜑𝜓))
63, 5eximii 1937 . . 3 𝑥(𝜑𝜓)
71, 619.36i 2276 . 2 (∀𝑥𝜑𝜓)
8 bj-vtoclf.min . 2 𝜑
97, 8mpg 1898 1 𝜓
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198   = wceq 1658  Ⅎwnf 1884   ∈ wcel 2166 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-12 2222 This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1881  df-nf 1885  df-clel 2822 This theorem is referenced by:  bj-vtocl  33432
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