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Theorem axsep 5193
 Description: Axiom scheme of separation ax-sep 5194 derived from the axiom scheme of replacement ax-rep 5181. The statement is identical to that of ax-sep 5194, and therefore shows that ax-sep 5194 is redundant when ax-rep 5181 is allowed. See ax-sep 5194 for more information. (Contributed by NM, 11-Sep-2006.) Use ax-sep 5194 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 5192 1 𝑦𝑥(𝑥𝑦 ↔ (𝑥𝑧𝜑))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 208   ∧ wa 398  ∀wal 1528  ∃wex 1773 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-rep 5181 This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1774  df-mo 2616  df-eu 2648  df-rex 3142 This theorem is referenced by: (None)
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