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Theorem bj-csbsn 34118
Description: Substitution in a singleton. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
bj-csbsn 𝐴 / 𝑥{𝑥} = {𝐴}

Proof of Theorem bj-csbsn
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 bj-csbsnlem 34117 . . 3 𝑦 / 𝑥{𝑥} = {𝑦}
21csbeq2i 3888 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑦{𝑦}
3 csbcow 3895 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑥{𝑥}
4 bj-csbsnlem 34117 . 2 𝐴 / 𝑦{𝑦} = {𝐴}
52, 3, 43eqtr3i 2849 1 𝐴 / 𝑥{𝑥} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  csb 3880  {csn 4557
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-sbc 3770  df-csb 3881  df-sn 4558
This theorem is referenced by:  bj-snsetex  34172
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