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Also converse is true:

- For each
`a`*`b`, left hand side of only*one*equation "matches":- Either
`b`= 0 or`b`=`y`' for some`y`. - Consequence of first Peano axiom.

- Either
- Equality
`b`=`y`' determines*unique*`y`.- (
`b`=`y`_{0}' /\`b`=`y`_{1}') =>`y`_{0}=`y`_{1}for all`y`_{0}and`y`_{1}. - Consequence of second Peano axiom.

- (

*Pair of equations uniquely determines a function.*

Author: Wolfgang Schreiner

Last Modification: November 24, 1999