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Mirrors > Home > MPE Home > Th. List > elALT | Structured version Visualization version GIF version |
Description: Alternate proof of el 5448, shorter but requiring ax-sep 5302. (Contributed by NM, 4-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
elALT | ⊢ ∃𝑦 𝑥 ∈ 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3482 | . 2 ⊢ 𝑥 ∈ V | |
2 | selsALT 5450 | . 2 ⊢ (𝑥 ∈ V → ∃𝑦 𝑥 ∈ 𝑦) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃𝑦 𝑥 ∈ 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1776 ∈ wcel 2106 Vcvv 3478 |
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-8 2108 ax-9 2116 ax-ext 2706 ax-sep 5302 ax-pr 5438 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-un 3968 df-sn 4632 df-pr 4634 |
This theorem is referenced by: (None) |
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