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Mirrors > Home > MPE Home > Th. List > p0exALT | Structured version Visualization version GIF version |
Description: Alternate proof of p0ex 5291 which is quite different and longer if snexALT 5290 is expanded. (Contributed by NM, 23-Dec-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
p0exALT | ⊢ {∅} ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snexALT 5290 | 1 ⊢ {∅} ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2111 Vcvv 3420 ∅c0 4251 {csn 4555 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2113 ax-9 2121 ax-ext 2709 ax-sep 5206 ax-nul 5213 ax-pow 5272 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2072 df-clab 2716 df-cleq 2730 df-clel 2817 df-rab 3071 df-v 3422 df-dif 3883 df-in 3887 df-ss 3897 df-nul 4252 df-pw 4529 df-sn 4556 |
This theorem is referenced by: (None) |
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