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Theorem gm-sbtru 35695
 Description: Substitution does not change truth. (Contributed by Giovanni Mascellani, 24-May-2019.)
Hypothesis
Ref Expression
gm-sbtru.1 𝐴 ∈ V
Assertion
Ref Expression
gm-sbtru ([𝐴 / 𝑥]⊤ ↔ ⊤)

Proof of Theorem gm-sbtru
StepHypRef Expression
1 gm-sbtru.1 . 2 𝐴 ∈ V
2 sbcg 3795 . 2 (𝐴 ∈ V → ([𝐴 / 𝑥]⊤ ↔ ⊤))
31, 2ax-mp 5 1 ([𝐴 / 𝑥]⊤ ↔ ⊤)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 209  ⊤wtru 1539   ∈ wcel 2111  Vcvv 3442  [wsbc 3722 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 2113  ax-9 2121  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-sbc 3723 This theorem is referenced by: (None)
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