Theorem frege55lem2a

Description: Core proof of Proposition 55 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege55lem2a	$$⊢\left(\phi \leftrightarrow \psi \right)\to if-\left(\psi ,\phi ,\neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bicom1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\psi \leftrightarrow \phi \right)$$
2		frege54cor0a	$$⊢\left(\psi \leftrightarrow \phi \right)\leftrightarrow if-\left(\psi ,\phi ,\neg \phi \right)$$
3	1 2	sylib	$$⊢\left(\phi \leftrightarrow \psi \right)\to if-\left(\psi ,\phi ,\neg \phi \right)$$