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Mirrors > Home > MPE Home > Th. List > iseqsetvlem | Structured version Visualization version GIF version |
Description: Lemma for iseqsetv-cleq 2802. (Contributed by Wolf Lammen, 17-Aug-2025.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
iseqsetvlem | ⊢ (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2737 | . 2 ⊢ (𝑥 = 𝑧 → (𝑥 = 𝐴 ↔ 𝑧 = 𝐴)) | |
2 | 1 | cbvexvw 2032 | 1 ⊢ (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 206 = wceq 1535 ∃wex 1774 |
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-9 2114 ax-ext 2704 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1775 df-cleq 2725 |
This theorem is referenced by: iseqsetv-cleq 2802 |
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