Consider the statement
Q are statements, and
⊤ denotes the tautology (true) statement. It seems intuitively true that the above biconditional statement is true. But I would like to prove it.
One direction is easy enough to prove: suppose
Q≡⊤; then by substitution, we have
P∧Q ≡ P∧⊤ ≡ P
by the identity law for conjunction.
However, the converse seems trickier. By assuming
P∧Q≡P, how would one know for certain that
Thanks in advance for your thoughts.
(P.S. Is it improper of me to use two different symbols for equivalence here?)