Theorem pm5.15 1014

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 382	. . 3 ⊢ (¬ (𝜑 ↔ 𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
2	1	biimpi 216	. 2 ⊢ (¬ (𝜑 ↔ 𝜓) → (𝜑 ↔ ¬ 𝜓))
3	2	orri 862	1 ⊢ ((𝜑 ↔ 𝜓) ∨ (𝜑 ↔ ¬ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 206   ∨ wo 847

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 207  df-or 848

This theorem is referenced by:  sbc2or  3770