Theorem mpteq12dvOLD

Description: Obsolete version of mpteq12dv as of 1-Dec-2023. (Contributed by NM, 24-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	mpteq12dv.1	⊢ ( 𝜑 → 𝐴 = 𝐶 )
	mpteq12dv.2	⊢ ( 𝜑 → 𝐵 = 𝐷 )
Assertion	mpteq12dvOLD	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐶 ↦ 𝐷 ) )

Proof

Step	Hyp	Ref	Expression
1		mpteq12dv.1	⊢ ( 𝜑 → 𝐴 = 𝐶 )
2		mpteq12dv.2	⊢ ( 𝜑 → 𝐵 = 𝐷 )
3	2	adantr	⊢ ( ( 𝜑 ∧ 𝑥 ∈ 𝐴 ) → 𝐵 = 𝐷 )
4	1 3	mpteq12dva	⊢ ( 𝜑 → ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = ( 𝑥 ∈ 𝐶 ↦ 𝐷 ) )