Theorem xorcomOLD 1510

Description: Obsolete version of xorcom 1509 as of 21-Apr-2024. (Contributed by Mario Carneiro, 4-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem xorcomOLD

Step	Hyp	Ref	Expression
1		bicom 221	. . 3 ⊢ ((𝜑 ↔ 𝜓) ↔ (𝜓 ↔ 𝜑))
2	1	notbii 320	. 2 ⊢ (¬ (𝜑 ↔ 𝜓) ↔ ¬ (𝜓 ↔ 𝜑))
3		df-xor 1507	. 2 ⊢ ((𝜑 ⊻ 𝜓) ↔ ¬ (𝜑 ↔ 𝜓))
4		df-xor 1507	. 2 ⊢ ((𝜓 ⊻ 𝜑) ↔ ¬ (𝜓 ↔ 𝜑))
5	2, 3, 4	3bitr4i 303	1 ⊢ ((𝜑 ⊻ 𝜓) ↔ (𝜓 ⊻ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 205   ⊻ wxo 1506

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-xor 1507

This theorem is referenced by: (None)