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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 33419 | . 2 ⊢ ⟪𝐴, 𝐵⟫ = {{𝐴}, {𝐴, {𝐵}}} | |
2 | prex 5333 | . 2 ⊢ {{𝐴}, {𝐴, {𝐵}}} ∈ V | |
3 | 1, 2 | eqeltri 2909 | 1 ⊢ ⟪𝐴, 𝐵⟫ ∈ V |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2114 Vcvv 3494 {csn 4567 {cpr 4569 ⟪caltop 33417 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 ax-sep 5203 ax-nul 5210 ax-pr 5330 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-dif 3939 df-un 3941 df-nul 4292 df-sn 4568 df-pr 4570 df-altop 33419 |
This theorem is referenced by: elaltxp 33436 |
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