Theorem pm5.15 859

Description: Theorem *5.15 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 15-Oct-2013.)

Assertion

Ref	Expression
pm5.15	⊢ ((φ ↔ ψ) ∨ (φ ↔ ¬ ψ))

Proof of Theorem pm5.15

Step	Hyp	Ref	Expression
1		xor3 346	. . 3 ⊢ (¬ (φ ↔ ψ) ↔ (φ ↔ ¬ ψ))
2	1	biimpi 186	. 2 ⊢ (¬ (φ ↔ ψ) → (φ ↔ ¬ ψ))
3	2	orri 365	1 ⊢ ((φ ↔ ψ) ∨ (φ ↔ ¬ ψ))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176   ∨ wo 357

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-or 359

This theorem is used by:  sbc2or  3055