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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 31235 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | prex 4836 | . 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V | |
3 | 1, 2 | eqeltri 2684 | 1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1977 Vcvv 3173 {csn 4125 {cpr 4127 ⟪caltop 31233 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-dif 3543 df-un 3545 df-nul 3875 df-sn 4126 df-pr 4128 df-altop 31235 |
This theorem is referenced by: elaltxp 31252 |
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