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Theorem bj-issettruALTV 36816
Description: Moved to main as issettru 2815 and kept for the comments.

Weak version of isset 3491 without ax-ext 2704. (Contributed by BJ, 24-Apr-2024.) (Proof modification is discouraged.)

Assertion
Ref Expression
bj-issettruALTV (∃𝑥 𝑥 = 𝐴𝐴 ∈ {𝑦 ∣ ⊤})
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝐴(𝑦)

Proof of Theorem bj-issettruALTV
Dummy variable 𝑧 is distinct from all other variables.
StepHypRef Expression
1 iseqsetv-clel 2816 . 2 (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴)
2 issettru 2815 . 2 (∃𝑧 𝑧 = 𝐴𝐴 ∈ {𝑦 ∣ ⊤})
31, 2bitri 275 1 (∃𝑥 𝑥 = 𝐴𝐴 ∈ {𝑦 ∣ ⊤})
Colors of variables: wff setvar class
Syntax hints:  wb 206   = wceq 1535  wtru 1536  wex 1774  wcel 2104  {cab 2710
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1963  ax-7 2003  ax-8 2106
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1538  df-ex 1775  df-sb 2061  df-clab 2711  df-clel 2812
This theorem is referenced by: (None)
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