Theorem infeq1i

Description: Equality inference for infimum. (Contributed by AV, 2-Sep-2020)

	Ref	Expression
Hypothesis	infeq1i.1	⊢ 𝐵 = 𝐶
Assertion	infeq1i	⊢ inf ( 𝐵 , 𝐴 , 𝑅 ) = inf ( 𝐶 , 𝐴 , 𝑅 )

Proof

Step	Hyp	Ref	Expression
1		infeq1i.1	⊢ 𝐵 = 𝐶
2		infeq1	⊢ ( 𝐵 = 𝐶 → inf ( 𝐵 , 𝐴 , 𝑅 ) = inf ( 𝐶 , 𝐴 , 𝑅 ) )
3	1 2	ax-mp	⊢ inf ( 𝐵 , 𝐴 , 𝑅 ) = inf ( 𝐶 , 𝐴 , 𝑅 )