Theorem xorneg 1313

Description: ⊻ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

Ref	Expression
xorneg	⊢ ((¬ φ ⊻ ¬ ψ) ↔ (φ ⊻ ψ))

Proof of Theorem xorneg

Step	Hyp	Ref	Expression
1		xorneg1 1311	. 2 ⊢ ((¬ φ ⊻ ¬ ψ) ↔ ¬ (φ ⊻ ¬ ψ))
2		xorneg2 1312	. . 3 ⊢ ((φ ⊻ ¬ ψ) ↔ ¬ (φ ⊻ ψ))
3	2	con2bii 322	. 2 ⊢ ((φ ⊻ ψ) ↔ ¬ (φ ⊻ ¬ ψ))
4	1, 3	bitr4i 243	1 ⊢ ((¬ φ ⊻ ¬ ψ) ↔ (φ ⊻ ψ))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176   ⊻ wxo 1304

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-xor 1305

This theorem is used by:  hadnot  1393  had0  1403  mtp-xor  1536