Talk:Self-Distributive Law for Conditional

The subpage structure for this theorem is showing some gaping holes. I became aware of this because Soundness Theorem for Hilbert Proof System should not refer to Self-Distributive Law for Conditional/Formulation 1/Proof by Truth Table but rather a truth table proof of (the forward implication of) formulation 2. I don't see how that proof can easily be formatted into this structure though. — Lord_Farin (talk) 12:08, 7 April 2014 (UTC)

Is this: Self-Distributive Law for Conditional/Formulation 2 insufficient then? It shows the biconditional, split into two directions, so the forward direction should be okay to link to ? What am I missing? --prime mover (talk) 13:27, 7 April 2014 (UTC)

Because it is a soundness theorem, the formula should be shown explicitly to be valid for boolean interpretations. Natural deduction is not enough. — Lord_Farin (talk) 13:29, 7 April 2014 (UTC)