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Theorem bj-nfsab1 36202
Description: Remove dependency on ax-13 2365 from nfsab1 2711. UPDATE / TODO: nfsab1 2711 does not use ax-13 2365 either anymore; bj-nfsab1 36202 is shorter than nfsab1 2711 but uses ax-12 2163. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nfsab1 𝑥 𝑦 ∈ {𝑥𝜑}
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem bj-nfsab1
StepHypRef Expression
1 hbab1 2712 . 2 (𝑦 ∈ {𝑥𝜑} → ∀𝑥 𝑦 ∈ {𝑥𝜑})
21nf5i 2134 1 𝑥 𝑦 ∈ {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wnf 1777  wcel 2098  {cab 2703
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 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2704
This theorem is referenced by: (None)
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