[FOM] Completeness of FOL without contraposition

Guillermo Badia guillebadia89 at gmail.com
Sat Apr 26 19:28:17 EDT 2014

Is there a completeness proof for FOL not using contraposition? I mean, is
there a direct proof that validity implies provability in FOL in the spirit
of say Kalmar's method for PL? Thanks in advance for any help you can offer
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