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Mirrors > Home > MPE Home > Th. List > p0exALT | Structured version Visualization version GIF version |
Description: Alternate proof of p0ex 4984 which is quite different and longer if snexALT 4983 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 4983 | 1 ⊢ {∅} ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2145 Vcvv 3351 ∅c0 4063 {csn 4316 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 ax-sep 4915 ax-nul 4923 ax-pow 4974 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 835 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-v 3353 df-dif 3726 df-in 3730 df-ss 3737 df-nul 4064 df-pw 4299 df-sn 4317 |
This theorem is referenced by: (None) |
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