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| 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 35959 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
| 2 | prex 5437 | . 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V | |
| 3 | 1, 2 | eqeltri 2837 | 1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V |
| Colors of variables: wff setvar class |
| Syntax hints: ∈ wcel 2108 Vcvv 3480 {csn 4626 {cpr 4628 ⟪caltop 35957 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pr 5432 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-dif 3954 df-un 3956 df-nul 4334 df-sn 4627 df-pr 4629 df-altop 35959 |
| This theorem is referenced by: elaltxp 35976 |
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