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Mirrors > Home > MPE Home > Th. List > ceqsexvOLDOLD | Structured version Visualization version GIF version |
Description: Obsolete version of ceqsexv 3493 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 1918 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | ceqsexvOLD.1 | . 2 ⊢ 𝐴 ∈ V | |
3 | ceqsexvOLD.2 | . 2 ⊢ (𝑥 = 𝐴 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | ceqsex 3491 | 1 ⊢ (∃𝑥(𝑥 = 𝐴 ∧ 𝜑) ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ wa 397 = wceq 1542 ∃wex 1782 ∈ wcel 2107 Vcvv 3444 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-12 2172 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-ex 1783 df-nf 1787 df-clel 2811 |
This theorem is referenced by: (None) |
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