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Metamath Proof Explorer
Description: Theorem *5.15 of WhiteheadRussell p. 124. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 15-Oct-2013)
|
|
Ref |
Expression |
|
Assertion |
pm5.15 |
⊢ ( ( 𝜑 ↔ 𝜓 ) ∨ ( 𝜑 ↔ ¬ 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
xor3 |
⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜑 ↔ ¬ 𝜓 ) ) |
| 2 |
1
|
biimpi |
⊢ ( ¬ ( 𝜑 ↔ 𝜓 ) → ( 𝜑 ↔ ¬ 𝜓 ) ) |
| 3 |
2
|
orri |
⊢ ( ( 𝜑 ↔ 𝜓 ) ∨ ( 𝜑 ↔ ¬ 𝜓 ) ) |