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Theorem snjust 3821
 Description: Soundness justification theorem for df-sn 3822. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
snjust
Distinct variable groups:   ,   ,

Proof of Theorem snjust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2444 . . 3
21cbvabv 2557 . 2
3 eqeq1 2444 . . 3
43cbvabv 2557 . 2
52, 4eqtri 2458 1
 Colors of variables: wff set class Syntax hints:   wceq 1653  cab 2424 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431
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