Theorem infeq1d

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

	Ref	Expression
Hypothesis	infeq1d.1	$$⊢\phi \to B=C$$
Assertion	infeq1d	$$⊢\phi \to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$

Proof

Step	Hyp	Ref	Expression
1		infeq1d.1	$$⊢\phi \to B=C$$
2		infeq1	$$⊢B=C\to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$
3	1 2	syl	$$⊢\phi \to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$