Theorem supeq1i

Description: Equality inference for supremum. (Contributed by Paul Chapman, 22-Jun-2011)

	Ref	Expression
Hypothesis	supeq1i.1	⊢ 𝐵 = 𝐶
Assertion	supeq1i	⊢ sup ( 𝐵 , 𝐴 , 𝑅 ) = sup ( 𝐶 , 𝐴 , 𝑅 )

Proof

Step	Hyp	Ref	Expression
1		supeq1i.1	⊢ 𝐵 = 𝐶
2		supeq1	⊢ ( 𝐵 = 𝐶 → sup ( 𝐵 , 𝐴 , 𝑅 ) = sup ( 𝐶 , 𝐴 , 𝑅 ) )
3	1 2	ax-mp	⊢ sup ( 𝐵 , 𝐴 , 𝑅 ) = sup ( 𝐶 , 𝐴 , 𝑅 )