Reflexive Principle of Equality [RPE]

Symmetric Principle of Equality [SPE]

Transitive Principle of Equality [TPE]

Transformation Principle of Addition for Equality [TPAE]

Transformation Principle of Subtraction for Equality [TPSE]

Transformation Principle of Multiplication for Equality [TPME]

Transformation Principle of Division for Equality [TPDE]

Transformation Principle of Opposites for Equality [TPOE]

Transformation Principle of Reciprocals for Equality [TPRE]

Associative Principle of Addition [APA]

Associative Principle of Multiplication [APM]

Commutative Principle of Addition [CPA]

Commutative Principle of Multiplication [CPM]

Distributive Principle of Multiplication over Addition [DPMA]

Principle of Adding Zero [PA0]

Principle of Multiplying by Positive One [PM+1]

Positive one is not equal to zero.

Introductory Principle for Opposites [IPO]

Introductory Principle for Division [IPD]

Definition Principle of Subtraction [DPS]

Definition Principle of Reciprocals [DPR]