Theorem mpto2OLD 1535

Description: Obsolete version of mpto2 1534 as of 12-Nov-2017. (Contributed by David A. Wheeler, 3-Jul-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
mpto2OLD.1	⊢ φ
mpto2OLD.2	⊢ (φ ⊻ ψ)

Assertion

Ref	Expression
mpto2OLD	⊢ ¬ ψ

Proof of Theorem mpto2OLD

Step	Hyp	Ref	Expression
1		mpto2OLD.1	. 2 ⊢ φ
2		mpto2OLD.2	. . . . 5 ⊢ (φ ⊻ ψ)
3		df-xor 1305	. . . . 5 ⊢ ((φ ⊻ ψ) ↔ ¬ (φ ↔ ψ))
4	2, 3	mpbi 199	. . . 4 ⊢ ¬ (φ ↔ ψ)
5		nbbn 347	. . . 4 ⊢ ((¬ φ ↔ ψ) ↔ ¬ (φ ↔ ψ))
6	4, 5	mpbir 200	. . 3 ⊢ (¬ φ ↔ ψ)
7	6	con1bii 321	. 2 ⊢ (¬ ψ ↔ φ)
8	1, 7	mpbir 200	1 ⊢ ¬ ψ

Syntax hints:  ¬ wn 3   ↔ wb 176   ⊻ wxo 1304

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 177  df-xor 1305

This theorem is referenced by: (None)