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Theorem bnj1464 30888
 Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1464.1 (𝜓 → ∀𝑥𝜓)
bnj1464.2 (𝑥 = 𝐴 → (𝜑𝜓))
Assertion
Ref Expression
bnj1464 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜓))
Distinct variable groups:   𝑥,𝐴   𝑥,𝑉
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑥)

Proof of Theorem bnj1464
StepHypRef Expression
1 bnj1464.1 . . 3 (𝜓 → ∀𝑥𝜓)
21nf5i 2022 . 2 𝑥𝜓
3 bnj1464.2 . 2 (𝑥 = 𝐴 → (𝜑𝜓))
42, 3sbciegf 3461 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1479   = wceq 1481   ∈ wcel 1988  [wsbc 3429 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-9 1997  ax-10 2017  ax-12 2045  ax-13 2244  ax-ext 2600 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-v 3197  df-sbc 3430 This theorem is referenced by:  bnj1465  30889  bnj1468  30890
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