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Mirrors > Home > MPE Home > Th. List > p0exALT | Structured version Visualization version GIF version |
Description: Alternate proof of p0ex 5180 which is quite different and longer if snexALT 5179 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 5179 | 1 ⊢ {∅} ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2081 Vcvv 3437 ∅c0 4215 {csn 4476 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-8 2083 ax-9 2091 ax-10 2112 ax-11 2126 ax-12 2141 ax-ext 2769 ax-sep 5099 ax-nul 5106 ax-pow 5162 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-tru 1525 df-ex 1762 df-nf 1766 df-sb 2043 df-clab 2776 df-cleq 2788 df-clel 2863 df-nfc 2935 df-v 3439 df-dif 3866 df-in 3870 df-ss 3878 df-nul 4216 df-pw 4459 df-sn 4477 |
This theorem is referenced by: (None) |
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