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Theorem sbceq1a 3056
 Description: Equality theorem for class substitution. Class version of sbequ12 1919. (Contributed by NM, 26-Sep-2003.)
Assertion
Ref Expression
sbceq1a (x = A → (φ ↔ [̣A / xφ))

Proof of Theorem sbceq1a
StepHypRef Expression
1 sbid 1922 . 2 ([x / x]φφ)
2 dfsbcq2 3049 . 2 (x = A → ([x / x]φ ↔ [̣A / xφ))
31, 2syl5bbr 250 1 (x = A → (φ ↔ [̣A / xφ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642  [wsb 1648  [̣wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047 This theorem is referenced by:  sbceq2a  3057  elrabsf  3084  cbvralcsf  3198
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