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Mirrors > Home > MPE Home > Th. List > rexeqOLD | Structured version Visualization version GIF version |
Description: Obsolete version of raleq 3321 as of 9-Mar-2025. (Contributed by NM, 29-Oct-1995.) Remove usage of ax-10 2139, ax-11 2155, and ax-12 2175. (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 3337 | 1 ⊢ (𝐴 = 𝐵 → (∃𝑥 ∈ 𝐴 𝜑 ↔ ∃𝑥 ∈ 𝐵 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 206 = wceq 1537 ∃wrex 3068 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1777 df-cleq 2727 df-rex 3069 |
This theorem is referenced by: (None) |
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