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Theorem spsbe 2075
 Description: A specialization theorem. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
spsbe ([y / x]φxφ)

Proof of Theorem spsbe
StepHypRef Expression
1 stdpc4 2024 . . . 4 (x ¬ φ → [y / x] ¬ φ)
2 sbn 2062 . . . 4 ([y / x] ¬ φ ↔ ¬ [y / x]φ)
31, 2sylib 188 . . 3 (x ¬ φ → ¬ [y / x]φ)
43con2i 112 . 2 ([y / x]φ → ¬ x ¬ φ)
5 df-ex 1542 . 2 (xφ ↔ ¬ x ¬ φ)
64, 5sylibr 203 1 ([y / x]φxφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  ∃wex 1541  [wsb 1648 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by: (None)
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