1090-11s-a

# 1090-11s-a - Axioms of Predicate Logic All partial...

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Axioms of Predicate Logic All partial generalizations of formulas in Ax1–Ax6 are axioms of Predicate Logic. Ax1 Every tautology of Predicate Logic Ax2 ( x ) A A [ x := t ], if deﬁned Ax3 ( x )( A B ) ( x ) A ( x ) B Ax4 A ( x ) A , provided x dnof in A Ax5 (Reﬂexivity of =) x = x Ax6 (Leibniz for =) s = t ( A [ x := s ] A [ x := t ] ) , if deﬁned Theorems of Predicate Logic Deﬁnition of ( x ) A ≡ ¬ ( x ) ¬ A 6.1.7 (Distributivity of over ) ( x )( A B ) ( x ) A ( x ) B Distributivity of over ( x )( A B ) ( x ) A ( x ) B 6.1.8 ( x )( y ) A ( y )( x ) A 6.4.1 ( x )( A B ) A ( x ) B , provided x dnof in A 6.4.2 ( x )( A B ) A ( x ) B , provided x dnof in A 6.4.3 ( x )( A B ) A ( x ) B , provided x dnof in A 6.4.4 (Dummy Renaming for ) ( x ) A ( y ) A [ x := y ], provided
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## This note was uploaded on 07/31/2011 for the course MATH 1090 taught by Professor Georgetourlakis during the Spring '09 term at York University.

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