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Theorem spsbbi 2077
Description: Specialization of biconditional. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
spsbbi (x(φψ) → ([y / x]φ ↔ [y / x]ψ))

Proof of Theorem spsbbi
StepHypRef Expression
1 stdpc4 2024 . 2 (x(φψ) → [y / x](φψ))
2 sbbi 2071 . 2 ([y / x](φψ) ↔ ([y / x]φ ↔ [y / x]ψ))
31, 2sylib 188 1 (x(φψ) → ([y / x]φ ↔ [y / x]ψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540  [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:  sbbid  2078  sbco3  2088
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