# Category:Rule of Material Equivalence

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This category contains pages concerning **Rule of Material Equivalence**:

The **rule of material equivalence** is a valid deduction sequent in propositional logic:

- If we can conclude that $p$ implies $q$ and if we can also conclude that $q$ implies $p$, then we may infer that $p$ if and only if $q$.

#### Formulation 1

- $p \iff q \dashv \vdash \paren {p \implies q} \land \paren {q \implies p}$

#### Formulation 2

- $\vdash \paren {p \iff q} \iff \paren {\paren {p \implies q} \land \paren {q \implies p} }$

## Pages in category "Rule of Material Equivalence"

The following 7 pages are in this category, out of 7 total.

### R

- Rule of Material Equivalence
- Rule of Material Equivalence/Formulation 1
- Rule of Material Equivalence/Formulation 1/Proof 1
- Rule of Material Equivalence/Formulation 1/Proof by Truth Table
- Rule of Material Equivalence/Formulation 2
- Rule of Material Equivalence/Formulation 2/Proof 1
- Rule of Material Equivalence/Formulation 2/Proof by Truth Table