Theorem ressle

Description: le is unaffected by restriction. (Contributed by Mario Carneiro, 3-Nov-2015)

	Ref	Expression
Hypotheses	ressle.1	⊢ 𝑊 = ( 𝐾 ↾s 𝐴 )
	ressle.2	⊢ ≤ = ( le ‘ 𝐾 )
Assertion	ressle	⊢ ( 𝐴 ∈ 𝑉 → ≤ = ( le ‘ 𝑊 ) )

Proof

Step	Hyp	Ref	Expression
1		ressle.1	⊢ 𝑊 = ( 𝐾 ↾s 𝐴 )
2		ressle.2	⊢ ≤ = ( le ‘ 𝐾 )
3		df-ple	⊢ le = Slot ; 1 0
4		10nn	⊢ ; 1 0 ∈ ℕ
5		1lt10	⊢ 1 < ; 1 0
6	1 2 3 4 5	resslem	⊢ ( 𝐴 ∈ 𝑉 → ≤ = ( le ‘ 𝑊 ) )