Theorem supeq1d

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

	Ref	Expression
Hypothesis	supeq1d.1	$$⊢\phi \to B=C$$
Assertion	supeq1d	$$⊢\phi \to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$

Proof

Step	Hyp	Ref	Expression
1		supeq1d.1	$$⊢\phi \to B=C$$
2		supeq1	$$⊢B=C\to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$
3	1 2	syl	$$⊢\phi \to sup\left(B,A,R\right)=sup\left(C,A,R\right)$$