Theorem xorcomOLD

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

	Ref	Expression
Assertion	xorcomOLD	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ( 𝜓 ⊻ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		bicom	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜓 ↔ 𝜑 ) )
2	1	notbii	⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜓 ↔ 𝜑 ) )
3		df-xor	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) )
4		df-xor	⊢ ( ( 𝜓 ⊻ 𝜑 ) ↔ ¬ ( 𝜓 ↔ 𝜑 ) )
5	2 3 4	3bitr4i	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ( 𝜓 ⊻ 𝜑 ) )