Metamath Proof Explorer

Theorem iotaequ

Description: Theorem *14.2 in WhiteheadRussell p. 189. (Contributed by Andrew Salmon, 11-Jul-2011)

Ref Expression
Assertion iotaequ 
|- ( iota x x = y ) = y

Proof

Step Hyp Ref Expression
1 iotaval 
 |-  ( A. x ( x = y <-> x = y ) -> ( iota x x = y ) = y )
2 biid 
 |-  ( x = y <-> x = y )
3 1 2 mpg 
 |-  ( iota x x = y ) = y