Theorem xorbi12iOLD

Description: Obsolete version of xorbi12i as of 21-Apr-2024. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	xorbi12.1	$$⊢\phi \leftrightarrow \psi$$
	xorbi12.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	xorbi12iOLD	$$⊢\left(\phi ⊻\chi \right)\leftrightarrow \left(\psi ⊻\theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		xorbi12.1	$$⊢\phi \leftrightarrow \psi$$
2		xorbi12.2	$$⊢\chi \leftrightarrow \theta$$
3	1 2	bibi12i	$$⊢\left(\phi \leftrightarrow \chi \right)\leftrightarrow \left(\psi \leftrightarrow \theta \right)$$
4	3	notbii	$$⊢\neg \left(\phi \leftrightarrow \chi \right)\leftrightarrow \neg \left(\psi \leftrightarrow \theta \right)$$
5		df-xor	$$⊢\left(\phi ⊻\chi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \chi \right)$$
6		df-xor	$$⊢\left(\psi ⊻\theta \right)\leftrightarrow \neg \left(\psi \leftrightarrow \theta \right)$$
7	4 5 6	3bitr4i	$$⊢\left(\phi ⊻\chi \right)\leftrightarrow \left(\psi ⊻\theta \right)$$