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Theorem axsep 5166
Description: Axiom scheme of separation ax-sep 5167 derived from the axiom scheme of replacement ax-rep 5154. The statement is identical to that of ax-sep 5167, and therefore shows that ax-sep 5167 is redundant when ax-rep 5154 is allowed. See ax-sep 5167 for more information. (Contributed by NM, 11-Sep-2006.) Use ax-sep 5167 instead. (New usage is discouraged.)
Assertion
Ref Expression
axsep 𝑦𝑥(𝑥𝑦 ↔ (𝑥𝑧𝜑))
Distinct variable groups:   𝑥,𝑦,𝑧   𝜑,𝑦,𝑧
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem axsep
StepHypRef Expression
1 axsepgfromrep 5165 1 𝑦𝑥(𝑥𝑦 ↔ (𝑥𝑧𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399  wal 1540  wex 1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-rep 5154
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787  df-mo 2540  df-eu 2570  df-rex 3059
This theorem is referenced by: (None)
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