Theorem cnveqd

Description: Equality deduction for converse relation. (Contributed by NM, 6-Dec-2013)

	Ref	Expression
Hypothesis	cnveqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	cnveqd	⊢ ( 𝜑 → ◡ 𝐴 = ◡ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		cnveqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		cnveq	⊢ ( 𝐴 = 𝐵 → ◡ 𝐴 = ◡ 𝐵 )
3	1 2	syl	⊢ ( 𝜑 → ◡ 𝐴 = ◡ 𝐵 )