Theorem infeq1

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

	Ref	Expression
Assertion	infeq1	|- ( B = C -> inf ( B , A , R ) = inf ( C , A , R ) )

Proof

Step	Hyp	Ref	Expression
1		supeq1	|- ( B = C -> sup ( B , A , `' R ) = sup ( C , A , `' R ) )
2		df-inf	|- inf ( B , A , R ) = sup ( B , A , `' R )
3		df-inf	|- inf ( C , A , R ) = sup ( C , A , `' R )
4	1 2 3	3eqtr4g	|- ( B = C -> inf ( B , A , R ) = inf ( C , A , R ) )