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Theorem bnj525 32123
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 3796 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  wcel 2112  Vcvv 3444  [wsbc 3723
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-12 2176  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-sbc 3724
This theorem is referenced by:  bnj976  32163  bnj91  32247  bnj92  32248  bnj523  32273  bnj539  32277  bnj540  32278  bnj1040  32358
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