Theorem ifid

Description: Identical true and false arguments in the conditional operator. (Contributed by NM, 18-Apr-2005)

	Ref	Expression
Assertion	ifid	$$⊢if\left(\phi ,A,A\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		iftrue	$$⊢\phi \to if\left(\phi ,A,A\right)=A$$
2		iffalse	$$⊢\neg \phi \to if\left(\phi ,A,A\right)=A$$
3	1 2	pm2.61i	$$⊢if\left(\phi ,A,A\right)=A$$