Theorem 1pr

Description: The positive real number 'one'. (Contributed by NM, 13-Mar-1996) (Revised by Mario Carneiro, 12-Jun-2013) (New usage is discouraged.)

	Ref	Expression
Assertion	1pr	$$⊢1_{𝑷}\in 𝑷$$

Proof

Step	Hyp	Ref	Expression
1		df-1p	$$⊢1_{𝑷}=\left\{x|x{<}_{𝑸}{1}_{𝑸}\right\}$$
2		1nq	$$⊢1_{𝑸}\in 𝑸$$
3		nqpr	$$⊢1_{𝑸}\in 𝑸\to \left\{x|x{<}_{𝑸}{1}_{𝑸}\right\}\in 𝑷$$
4	2 3	ax-mp	$$⊢\left\{x|x{<}_{𝑸}{1}_{𝑸}\right\}\in 𝑷$$
5	1 4	eqeltri	$$⊢1_{𝑷}\in 𝑷$$