Full Idea
The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'.
Gist of Idea
'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)'
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.3)
Book Reference
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.26
A Reaction
So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities.