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Mirrors > Home > MPE Home > Th. List > elissetOLD | Structured version Visualization version GIF version |
Description: Obsolete version of elisset 3505 as of 28-Aug-2023. An element of a class exists. (Contributed by NM, 1-May-1995.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
elissetOLD | ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3512 | . 2 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ V) | |
2 | isset 3506 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | sylib 220 | 1 ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∃wex 1780 ∈ wcel 2114 Vcvv 3494 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-v 3496 |
This theorem is referenced by: (None) |
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