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		pleid	⊢ le = Slot ( le ‘ ndx )
4		plendxnbasendx	⊢ ( le ‘ ndx ) ≠ ( Base ‘ ndx )
5	1 2 3 4	resseqnbas	⊢ ( 𝐴 ∈ 𝑉 → ≤ = ( le ‘ 𝑊 ) )