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Theorem bj-csbsn 32599
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 32598 . . 3 𝑦 / 𝑥{𝑥} = {𝑦}
21csbeq2i 3971 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑦{𝑦}
3 csbco 3529 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑥{𝑥}
4 bj-csbsnlem 32598 . 2 𝐴 / 𝑦{𝑦} = {𝐴}
52, 3, 43eqtr3i 2651 1 𝐴 / 𝑥{𝑥} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  csb 3519  {csn 4155
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3192  df-sbc 3423  df-csb 3520  df-sn 4156
This theorem is referenced by:  bj-snsetex  32651
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