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Theorem bnj525 31259
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 3664 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 197  wcel 2155  Vcvv 3350  [wsbc 3598
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-12 2211  ax-13 2352  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-v 3352  df-sbc 3599
This theorem is referenced by:  bnj976  31299  bnj91  31382  bnj92  31383  bnj523  31408  bnj539  31412  bnj540  31413  bnj1040  31491
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