Theorem bj-mndsssmgrp

Description: Monoids are semigroups. (Contributed by BJ, 11-Apr-2024) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-mndsssmgrp	⊢ Mnd ⊆ Smgrp

Proof

Step	Hyp	Ref	Expression
1		df-mnd	⊢ Mnd = { 𝑔 ∈ Smgrp ∣ [ ( Base ‘ 𝑔 ) / 𝑏 ] [ ( +g ‘ 𝑔 ) / 𝑝 ] ∃ 𝑒 ∈ 𝑏 ∀ 𝑥 ∈ 𝑏 ( ( 𝑒 𝑝 𝑥 ) = 𝑥 ∧ ( 𝑥 𝑝 𝑒 ) = 𝑥 ) }
2	1	ssrab3	⊢ Mnd ⊆ Smgrp