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| Mirrors > Home > MPE Home > Th. List > iseqsetvlem | Structured version Visualization version GIF version | ||
| Description: Lemma for iseqsetv-cleq 2805. (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 2740 | . 2 ⊢ (𝑥 = 𝑧 → (𝑥 = 𝐴 ↔ 𝑧 = 𝐴)) | |
| 2 | 1 | cbvexvw 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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