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Theorem sbcbidv 3100
 Description: Formula-building deduction rule for class substitution. (Contributed by NM, 29-Dec-2014.)
Hypothesis
Ref Expression
sbcbidv.1 (φ → (ψχ))
Assertion
Ref Expression
sbcbidv (φ → ([̣A / xψ ↔ [̣A / xχ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem sbcbidv
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 sbcbidv.1 . 2 (φ → (ψχ))
31, 2sbcbid 3099 1 (φ → ([̣A / xψ ↔ [̣A / xχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  [̣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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047 This theorem is referenced by:  sbcbii  3101  csbcomg  3159  opelopabsb  4697  opelopabf  4711
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