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Metamath Proof Explorer

Theorem funcnvcnv

Description: The double converse of a function is a function. (Contributed by NM, 21-Sep-2004)

Ref Expression
Assertion funcnvcnv 
|- ( Fun A -> Fun `' `' A )

Proof

Step Hyp Ref Expression
1 cnvcnvss 
 |-  `' `' A C_ A
2 funss 
 |-  ( `' `' A C_ A -> ( Fun A -> Fun `' `' A ) )
3 1 2 ax-mp 
 |-  ( Fun A -> Fun `' `' A )