![]() |
Mathbox for Scott Fenton |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > altopex | Structured version Visualization version GIF version |
Description: Alternative ordered pairs always exist. (Contributed by Scott Fenton, 22-Mar-2012.) |
Ref | Expression |
---|---|
altopex | ⊢ ⟪𝐴, 𝐵⟫ ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-altop 32402 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | prex 5038 | . 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V | |
3 | 1, 2 | eqeltri 2846 | 1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2145 Vcvv 3351 {csn 4317 {cpr 4319 ⟪caltop 32400 |
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 4916 ax-nul 4924 ax-pr 5035 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 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-un 3728 df-nul 4064 df-sn 4318 df-pr 4320 df-altop 32402 |
This theorem is referenced by: elaltxp 32419 |
Copyright terms: Public domain | W3C validator |