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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 32668 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | prex 5141 | . 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V | |
3 | 1, 2 | eqeltri 2854 | 1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2106 Vcvv 3397 {csn 4397 {cpr 4399 ⟪caltop 32666 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2054 ax-9 2115 ax-10 2134 ax-11 2149 ax-12 2162 ax-ext 2753 ax-sep 5017 ax-nul 5025 ax-pr 5138 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2763 df-cleq 2769 df-clel 2773 df-nfc 2920 df-v 3399 df-dif 3794 df-un 3796 df-nul 4141 df-sn 4398 df-pr 4400 df-altop 32668 |
This theorem is referenced by: elaltxp 32685 |
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