Theorem infeq2

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

	Ref	Expression
Assertion	infeq2	|- ( B = C -> inf ( A , B , R ) = inf ( A , C , R ) )

Proof

Step	Hyp	Ref	Expression
1		supeq2	|- ( B = C -> sup ( A , B , `' R ) = sup ( A , C , `' R ) )
2		df-inf	|- inf ( A , B , R ) = sup ( A , B , `' R )
3		df-inf	|- inf ( A , C , R ) = sup ( A , C , `' R )
4	1 2 3	3eqtr4g	|- ( B = C -> inf ( A , B , R ) = inf ( A , C , R ) )