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Metamath Proof Explorer

Theorem psr1bas2

Description: The base set of the ring of univariate power series. (Contributed by Mario Carneiro, 3-Jul-2015)

Step	Hyp	Ref	Expression
1		psr1val.1	$⊢ S = {PwSer}_{1} (R)$
2		psr1bas2.b	$⊢ B = {Base}_{S}$
3		psr1bas2.o	$⊢ O = 1_{𝑜} mPwSer R$
4	1	psr1val	$⊢ S = (1_{𝑜} ordPwSer R) (\emptyset)$
5		0ss	$⊢ \emptyset \subseteq 1_{𝑜} \times 1_{𝑜}$
6	5	a1i	$⊢ ⊤ \to \emptyset \subseteq 1_{𝑜} \times 1_{𝑜}$
7	3 4 6	opsrbas	$⊢ ⊤ \to {Base}_{O} = {Base}_{S}$
8	7	mptru	$⊢ {Base}_{O} = {Base}_{S}$
9	2 8	eqtr4i	$⊢ B = {Base}_{O}$