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Theorem bj-csbsn 36847
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 36846 . . 3 𝑦 / 𝑥{𝑥} = {𝑦}
21csbeq2i 3916 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑦{𝑦}
3 csbcow 3923 . 2 𝐴 / 𝑦𝑦 / 𝑥{𝑥} = 𝐴 / 𝑥{𝑥}
4 bj-csbsnlem 36846 . 2 𝐴 / 𝑦{𝑦} = {𝐴}
52, 3, 43eqtr3i 2769 1 𝐴 / 𝑥{𝑥} = {𝐴}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1535  csb 3908  {csn 4630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106  ax-9 2114  ax-10 2137  ax-12 2173  ax-ext 2704
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1538  df-ex 1775  df-nf 1779  df-sb 2061  df-clab 2711  df-cleq 2725  df-clel 2812  df-v 3479  df-sbc 3792  df-csb 3909  df-sn 4631
This theorem is referenced by:  bj-snsetex  36906
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