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Theorem bnj525 31035
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 3609 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]𝜑𝜑))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wcel 2103  Vcvv 3304  [wsbc 3541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-12 2160  ax-13 2355  ax-ext 2704
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-v 3306  df-sbc 3542
This theorem is referenced by:  bnj538OLD  31038  bnj976  31076  bnj91  31159  bnj92  31160  bnj523  31185  bnj539  31189  bnj540  31190  bnj1040  31268
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