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Theorem sbsbc 3050
 Description: Show that df-sb 1649 and df-sbc 3047 are equivalent when the class term A in df-sbc 3047 is a setvar variable. This theorem lets us reuse theorems based on df-sb 1649 for proofs involving df-sbc 3047. (Contributed by NM, 31-Dec-2016.) (Proof modification is discouraged.)
Assertion
Ref Expression
sbsbc ([y / x]φ ↔ [̣y / xφ)

Proof of Theorem sbsbc
StepHypRef Expression
1 eqid 2353 . 2 y = y
2 dfsbcq2 3049 . 2 (y = y → ([y / x]φ ↔ [̣y / xφ))
31, 2ax-mp 5 1 ([y / x]φ ↔ [̣y / xφ)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176  [wsb 1648  [̣wsbc 3046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047 This theorem is referenced by:  spsbc  3058  sbcid  3062  sbcco  3068  sbcco2  3069  sbcie2g  3079  eqsbc3  3085  sbcralt  3118  csbid  3143  sbnfc2  3196  csbabg  3197  cbvralcsf  3198  cbvreucsf  3200  cbvrabcsf  3201
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