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Theorem bj-csbsn 33256
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 33255 . . 3 𝑦 / 𝑥{𝑥} = {𝑦}
21csbeq2i 4154 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑦{𝑦}
3 csbco 3701 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑥{𝑥}
4 bj-csbsnlem 33255 . 2 𝐴 / 𝑦{𝑦} = {𝐴}
52, 3, 43eqtr3i 2795 1 𝐴 / 𝑥{𝑥} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1652  csb 3691  {csn 4334
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2352  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-sbc 3597  df-csb 3692  df-sn 4335
This theorem is referenced by:  bj-snsetex  33310
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