Description: Equality theorem for infimum. (Contributed by AV, 2-Sep-2020)
Ref | Expression | ||
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Assertion | infeq1 | |- ( B = C -> inf ( B , A , R ) = inf ( C , A , R ) ) |
Step | Hyp | Ref | Expression |
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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 ) |
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4 | 1 2 3 | 3eqtr4g | |- ( B = C -> inf ( B , A , R ) = inf ( C , A , R ) ) |