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Theorem elALT 5444
Description: Alternate proof of el 5441, shorter but requiring ax-sep 5295. (Contributed by NM, 4-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
elALT 𝑦 𝑥𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem elALT
StepHypRef Expression
1 vex 3483 . 2 𝑥 ∈ V
2 selsALT 5443 . 2 (𝑥 ∈ V → ∃𝑦 𝑥𝑦)
31, 2ax-mp 5 1 𝑦 𝑥𝑦
Colors of variables: wff setvar class
Syntax hints:  wex 1778  wcel 2107  Vcvv 3479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-sep 5295  ax-pr 5431
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-un 3955  df-sn 4626  df-pr 4628
This theorem is referenced by: (None)
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