If the product of an addition reaction is unstable under the reaction conditions and undergoes an elimination reaction, the overall reaction is called an addition-elimination.
eg:
mechanism:
The first stage of the mechanism, shown in black, is an acid-catalyzed addition. The addition product, hemiaminal 1, is unstable under acidic conditions and undergoes a 1,2-elimination, shown in blue, via activation of the hydroxy group by the acid. Thus, the overall reaction is an addition-elimination.
See also condensation reaction and addition-substitution.
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