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Mirrors > Home > MPE Home > Th. List > Mathboxes > mndoismgmOLD | Structured version Visualization version GIF version |
Description: Obsolete version of mndmgm 18402 as of 3-Feb-2020. A monoid is a magma. (Contributed by FL, 2-Nov-2009.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
mndoismgmOLD | ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mndoissmgrpOLD 36034 | . 2 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ SemiGrp) | |
2 | smgrpismgmOLD 36028 | . 2 ⊢ (𝐺 ∈ SemiGrp → 𝐺 ∈ Magma) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝐺 ∈ MndOp → 𝐺 ∈ Magma) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2106 Magmacmagm 36014 SemiGrpcsem 36026 MndOpcmndo 36032 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1542 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-v 3431 df-in 3893 df-sgrOLD 36027 df-mndo 36033 |
This theorem is referenced by: mndomgmid 36037 rngo1cl 36105 isdrngo2 36124 |
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