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| Mirrors > Home > MPE Home > Th. List > rexeqOLD | Structured version Visualization version GIF version | ||
| Description: Obsolete version of raleq 3323 as of 9-Mar-2025. (Contributed by NM, 29-Oct-1995.) Remove usage of ax-10 2141, ax-11 2157, and ax-12 2177. (Revised by Steven Nguyen, 30-Apr-2023.) (New usage is discouraged.) (Proof modification is discouraged.) |
| Ref | Expression |
|---|---|
| rexeqOLD | ⊢ (𝐴 = 𝐵 → (∃𝑥 ∈ 𝐴 𝜑 ↔ ∃𝑥 ∈ 𝐵 𝜑)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biidd 262 | . 2 ⊢ (𝐴 = 𝐵 → (𝜑 ↔ 𝜑)) | |
| 2 | 1 | rexeqbi1dv 3339 | 1 ⊢ (𝐴 = 𝐵 → (∃𝑥 ∈ 𝐴 𝜑 ↔ ∃𝑥 ∈ 𝐵 𝜑)) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ↔ wb 206 = wceq 1540 ∃wrex 3070 |
| 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 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-cleq 2729 df-rex 3071 |
| This theorem is referenced by: (None) |
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