(∃x)(Fx ⋅ Hx) ⊃ ~ (x)((Fx ∨ Gx) ⊃ ~ (Hx ∨ Gx))
A conditional a CP --Assume the antecedent and deduce the consequent
conditional a Universal/Conditional Proof -- Assume the
instantiation of the antecedent and deduce the consequent
Otherwise a Indirect Proof – Assume the negation of the conclusion and deduce a
contraction, thus proving the conclusion.
1. (∃x)(Fx ⋅ Hx) Assume
& (Gv V Hv) 1
3. Fv 2
V Hv 2
5. (∃x)(Fx) 3
V Hy) 4
& (∃x)(Gy V Hy) 5,
8. (∃x)[Fx & (Gx V Hx)]
É [(∃x)(Fx) & (∃x)(Gy
V Hy)] 1-7 CP
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