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Theorem bnj525 29855
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj525.1 𝐴 ∈ V
Assertion
Ref Expression
bnj525 ([𝐴 / 𝑥]𝜑𝜑)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem bnj525
StepHypRef Expression
1 bnj525.1 . 2 𝐴 ∈ V
2 sbcg 3470 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 195  wcel 1977  Vcvv 3173  [wsbc 3402
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-v 3175  df-sbc 3403
This theorem is referenced by:  bnj538OLD  29858  bnj976  29896  bnj91  29979  bnj92  29980  bnj523  30005  bnj539  30009  bnj540  30010  bnj1040  30088
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