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Theorem bj-cleljusti 33000
Description: One direction of cleljust 2152, requiring only ax-1 6-- ax-5 1990 and ax8v1 2148. (Contributed by BJ, 31-Dec-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-cleljusti (∃𝑧(𝑧 = 𝑥𝑧𝑦) → 𝑥𝑦)
Distinct variable groups:   𝑥,𝑧   𝑦,𝑧

Proof of Theorem bj-cleljusti
StepHypRef Expression
1 ax8v1 2148 . . 3 (𝑧 = 𝑥 → (𝑧𝑦𝑥𝑦))
21imp 393 . 2 ((𝑧 = 𝑥𝑧𝑦) → 𝑥𝑦)
32exlimiv 2009 1 (∃𝑧(𝑧 = 𝑥𝑧𝑦) → 𝑥𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wex 1851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-8 2146
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1852
This theorem is referenced by: (None)
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