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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-issettruALTV | Structured version Visualization version GIF version | ||
| Description: Moved to main as issettru 2818 and kept for the comments.
Weak version of isset 3493 without ax-ext 2707. (Contributed by BJ, 24-Apr-2024.) (Proof modification is discouraged.) |
| Ref | Expression |
|---|---|
| bj-issettruALTV | ⊢ (∃𝑥 𝑥 = 𝐴 ↔ 𝐴 ∈ {𝑦 ∣ ⊤}) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iseqsetv-clel 2819 | . 2 ⊢ (∃𝑥 𝑥 = 𝐴 ↔ ∃𝑧 𝑧 = 𝐴) | |
| 2 | issettru 2818 | . 2 ⊢ (∃𝑧 𝑧 = 𝐴 ↔ 𝐴 ∈ {𝑦 ∣ ⊤}) | |
| 3 | 1, 2 | bitri 275 | 1 ⊢ (∃𝑥 𝑥 = 𝐴 ↔ 𝐴 ∈ {𝑦 ∣ ⊤}) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 = wceq 1540 ⊤wtru 1541 ∃wex 1779 ∈ wcel 2108 {cab 2713 |
| 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-8 2110 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2714 df-clel 2815 |
| This theorem is referenced by: (None) |
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