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Theorem iseqsetvlem 2804
Description: Lemma for iseqsetv-cleq 2805. (Contributed by Wolf Lammen, 17-Aug-2025.) (Proof modification is discouraged.)
Assertion
Ref Expression
iseqsetvlem (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴)
Distinct variable group:   𝑥,𝑧,𝐴

Proof of Theorem iseqsetvlem
StepHypRef Expression
1 eqeq1 2740 . 2 (𝑥 = 𝑧 → (𝑥 = 𝐴𝑧 = 𝐴))
21cbvexvw 2036 1 (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1540  wex 1779
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-9 2118  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-cleq 2728
This theorem is referenced by:  iseqsetv-cleq  2805
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