Theorem ltrelpr

Description: Positive real 'less than' is a relation on positive reals. (Contributed by NM, 14-Feb-1996) (New usage is discouraged.)

	Ref	Expression
Assertion	ltrelpr	⊢ <P ⊆ ( P × P )

Proof

Step	Hyp	Ref	Expression
1		df-ltp	⊢ <P = { ⟨ 𝑥 , 𝑦 ⟩ ∣ ( ( 𝑥 ∈ P ∧ 𝑦 ∈ P ) ∧ 𝑥 ⊊ 𝑦 ) }
2		opabssxp	⊢ { ⟨ 𝑥 , 𝑦 ⟩ ∣ ( ( 𝑥 ∈ P ∧ 𝑦 ∈ P ) ∧ 𝑥 ⊊ 𝑦 ) } ⊆ ( P × P )
3	1 2	eqsstri	⊢ <P ⊆ ( P × P )