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Mirrors > Home > MPE Home > Th. List > ceqsexvOLDOLD | Structured version Visualization version GIF version |
Description: Obsolete version of ceqsexv 3516 as of 12-Oct-2024. (Contributed by NM, 2-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ceqsexvOLD.1 | ⊢ 𝐴 ∈ V |
ceqsexvOLD.2 | ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
ceqsexvOLDOLD | ⊢ (∃𝑥(𝑥 = 𝐴 ∧ 𝜑) ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1909 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | ceqsexvOLD.1 | . 2 ⊢ 𝐴 ∈ V | |
3 | ceqsexvOLD.2 | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | ceqsex 3514 | 1 ⊢ (∃𝑥(𝑥 = 𝐴 ∧ 𝜑) ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ wa 394 = wceq 1533 ∃wex 1773 ∈ wcel 2098 Vcvv 3463 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-12 2166 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-ex 1774 df-nf 1778 df-clel 2802 |
This theorem is referenced by: (None) |
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