Problem: Prove ( (
→
) →
) →
((A→B)→A)→A using axioms and hypothetical syllogism (HS).
Relevant Axioms:
Axiom 1 (A1):
→ (
→
)
Axiom 2 (A2): (
→ (
→
) ) → ( (
→
) → (
→
) )
Axiom 3 (A3): ( ¬
→ ¬
) → (
→
)
Hypothetical Syllogism (HS): If
→
and
→
, then
→
.
Attempt at a Solution:
1. (
→
) →
1.[Assumption for conditional proof]
2.
[Assumption for conditional proof]
3.
→ (
→
) [From Axiom 1]
4.
→
[Modus Ponens on lines 2 and 3]
5.
→
6.
[From line 2 and HS on lines 5 and 6]
However, I am not sure if this is correct or if I am using the axioms and HS properly. Could someone guide me through the correct steps to construct this proof?
Thank you for your assistance!
