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Theorem bj-csbsn 36883
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 36882 . . 3 𝑦 / 𝑥{𝑥} = {𝑦}
21csbeq2i 3906 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑦{𝑦}
3 csbcow 3913 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑥{𝑥}
4 bj-csbsnlem 36882 . 2 𝐴 / 𝑦{𝑦} = {𝐴}
52, 3, 43eqtr3i 2772 1 𝐴 / 𝑥{𝑥} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  csb 3898  {csn 4624
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-12 2177  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-sbc 3788  df-csb 3899  df-sn 4625
This theorem is referenced by:  bj-snsetex  36942
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