Theorem infeq1d

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

	Ref	Expression
Hypothesis	infeq1d.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
Assertion	infeq1d	⊢ ( 𝜑 → inf ( 𝐵 , 𝐴 , 𝑅 ) = inf ( 𝐶 , 𝐴 , 𝑅 ) )

Proof

Step	Hyp	Ref	Expression
1		infeq1d.1	⊢ ( 𝜑 → 𝐵 = 𝐶 )
2		infeq1	⊢ ( 𝐵 = 𝐶 → inf ( 𝐵 , 𝐴 , 𝑅 ) = inf ( 𝐶 , 𝐴 , 𝑅 ) )
3	1 2	syl	⊢ ( 𝜑 → inf ( 𝐵 , 𝐴 , 𝑅 ) = inf ( 𝐶 , 𝐴 , 𝑅 ) )