![]() |
Mathbox for Jeff Madsen |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > mndomgmid | Structured version Visualization version GIF version |
Description: A monoid is a magma with an identity element. (Contributed by FL, 18-Feb-2010.) (New usage is discouraged.) |
Ref | Expression |
---|---|
mndomgmid | ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId )) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mndoismgmOLD 37343 | . 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma) | |
2 | mndoisexid 37342 | . 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ ExId ) | |
3 | 1, 2 | elind 4194 | 1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ (Magma ∩ ExId )) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2099 ∩ cin 3946 ExId cexid 37317 Magmacmagm 37321 MndOpcmndo 37339 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-v 3473 df-in 3954 df-sgrOLD 37334 df-mndo 37340 |
This theorem is referenced by: ismndo2 37347 rngoidmlem 37409 isdrngo2 37431 |
Copyright terms: Public domain | W3C validator |