Theorem mtp-xorOLD 1537

Description: Obsolete version of mtp-xor 1536 as of 11-Nov-2017. (Contributed by David A. Wheeler, 4-Jul-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
mtp-xor.1	⊢ ¬ φ
mtp-xor.2	⊢ (φ ⊻ ψ)

Assertion

Ref	Expression
mtp-xorOLD	⊢ ψ

Proof of Theorem mtp-xorOLD

Step	Hyp	Ref	Expression
1		mtp-xor.1	. 2 ⊢ ¬ φ
2		mtp-xor.2	. . . . 5 ⊢ (φ ⊻ ψ)
3		df-xor 1305	. . . . 5 ⊢ ((φ ⊻ ψ) ↔ ¬ (φ ↔ ψ))
4	2, 3	mpbi 199	. . . 4 ⊢ ¬ (φ ↔ ψ)
5		bicom 191	. . . 4 ⊢ ((φ ↔ ψ) ↔ (ψ ↔ φ))
6	4, 5	mtbi 289	. . 3 ⊢ ¬ (ψ ↔ φ)
7		xor3 346	. . 3 ⊢ (¬ (ψ ↔ φ) ↔ (ψ ↔ ¬ φ))
8	6, 7	mpbi 199	. 2 ⊢ (ψ ↔ ¬ φ)
9	1, 8	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)