Define a propositional form as follows:
1) Lower case letters, along with lower case letters subscripted with numbers a1, b2, c13 are propositional forms.
2) If x and y are both propositional forms, then Cxy is a propositional form.
Let Cab denote the material conditional with 'a' and 'b' taking truth values in {T, F}. Let "C1 ...Cn" denote a concatenation of n conditionals, and "a1...a(n+1)" a concatenation of (n+1) logical variables. E. G. C1...C3a1...a4 denotes CCCa1a2a3a4. Let a/b denote a substitution of variable "a" with "b", let a/Cab denote that we substitute variable "a" with Cab.
Axiom 1: CCpqCCqrCpr
Axiom 2: CqCpq
Theorem 1: CCCpqC1...C(10^100)a1...a((10^100)+1)CqC1...C(10^100)a1...a((10^100)+1)
Demonstration:
1 CCqCpqCCCpqC1...C(10^100)a1...a((10^100)+1)CqC1...C(10^100)
a1...a((10^100)+1) Axiom 1, p/q, q/Cpq, r/C1...C(10^100)a1...a((10^100)+1)
2 CCCpqC1...C(10^100)a1...a((10^100)+1)CqC1...C(10^100)a1...a((10^100)+1) Axiom 2, 1 detachment.
Monday, September 19, 2011
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