Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-ralel | Structured version Visualization version GIF version |
Description: All elements of a class are elements of the class. (Contributed by Wolf Lammen, 10-Jun-2023.) |
Ref | Expression |
---|---|
wl-ralel | ⊢ ∀(𝑥 : 𝐴)𝑥 ∈ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝑥 ∈ 𝐴) | |
2 | 1 | wl-rgen 34877 | 1 ⊢ ∀(𝑥 : 𝐴)𝑥 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2113 ∀wl-ral 34866 |
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 1969 ax-7 2014 ax-8 2115 ax-11 2160 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1780 df-clel 2892 df-wl-ral 34871 |
This theorem is referenced by: (None) |
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