SOLUTION: Proving [F • (D ⊃ ∼F)] ⊃ (D ⊃ A) using the eighteen logical rules of inference

Algebra ->  Proofs -> SOLUTION: Proving [F • (D ⊃ ∼F)] ⊃ (D ⊃ A) using the eighteen logical rules of inference      Log On


   

Question 1205222: Proving [F • (D ⊃ ∼F)] ⊃ (D ⊃ A) using the eighteen logical rules of inference
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'll use the arrow --> in place of the horseshoe.
NumberStatementLine(s) UsedReason
:.[F * (D --> ~F)] --> (D --> A)
1F * (D --> ~F)Assumption for Conditional Proof
2F1Simplification
3D --> ~F1Simplification
4~(~F)2Double Negation
5~D3,4Modus Tollens
6~D v A5Addition
7D --> A6Material Implication
8[F * (D --> ~F)] --> (D --> A)1 - 7Conditional Proof

Here is the list of the rules of inference and rules of replacement
https://www.algebra.com/algebra/homework/Conjunction/logic-rules-of-inference-and-replacement.lesson