Theorem infeq1i

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

	Ref	Expression
Hypothesis	infeq1i.1	$$⊢B=C$$
Assertion	infeq1i	$$⊢sup\left(B,A,R\right)=sup\left(C,A,R\right)$$

Proof

Step	Hyp	Ref	Expression
1		infeq1i.1	$$⊢B=C$$
2		infeq1	$$⊢B=C\to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$
3	1 2	ax-mp	$$⊢sup\left(B,A,R\right)=sup\left(C,A,R\right)$$