Theorem int-mulsimpd

Description: MultiplicationSimplification generator rule. (Contributed by Stanislas Polu, 7-Apr-2020)

	Ref	Expression
Hypotheses	int-mulsimpd.1	⊢ ( 𝜑 → 𝐵 ∈ ℝ )
	int-mulsimpd.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
	int-mulsimpd.3	⊢ ( 𝜑 → 𝐵 ≠ 0 )
Assertion	int-mulsimpd	⊢ ( 𝜑 → 1 = ( 𝐴 / 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		int-mulsimpd.1	⊢ ( 𝜑 → 𝐵 ∈ ℝ )
2		int-mulsimpd.2	⊢ ( 𝜑 → 𝐴 = 𝐵 )
3		int-mulsimpd.3	⊢ ( 𝜑 → 𝐵 ≠ 0 )
4	1	recnd	⊢ ( 𝜑 → 𝐵 ∈ ℂ )
5	4 3 2	diveq1bd	⊢ ( 𝜑 → ( 𝐴 / 𝐵 ) = 1 )
6	5	eqcomd	⊢ ( 𝜑 → 1 = ( 𝐴 / 𝐵 ) )