Mathbox for Giovanni Mascellani < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  csbconstgi Structured version   Visualization version   GIF version

Theorem csbconstgi 33092
 Description: The proper substitution of a class for a variable in another variable does not modify it, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.)
Hypothesis
Ref Expression
csbconstgi.1 𝐴 ∈ V
Assertion
Ref Expression
csbconstgi 𝐴 / 𝑥𝑦 = 𝑦
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝐴(𝑥,𝑦)

Proof of Theorem csbconstgi
StepHypRef Expression
1 csbconstgi.1 . 2 𝐴 ∈ V
2 csbconstg 3512 . 2 (𝐴 ∈ V → 𝐴 / 𝑥𝑦 = 𝑦)
31, 2ax-mp 5 1 𝐴 / 𝑥𝑦 = 𝑦
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∈ wcel 1977  Vcvv 3173  ⦋csb 3499 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-10 2006  ax-11 2021  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-nfc 2740  df-v 3175  df-sbc 3403  df-csb 3500 This theorem is referenced by:  sbccom2lem  33099
 Copyright terms: Public domain W3C validator