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Metamath Proof Explorer
Description: Theorem *4.15 of WhiteheadRussell p. 117. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 18-Nov-2012)
|
|
Ref |
Expression |
|
Assertion |
pm4.15 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) → ¬ 𝜑 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
con2b |
⊢ ( ( ( 𝜓 ∧ 𝜒 ) → ¬ 𝜑 ) ↔ ( 𝜑 → ¬ ( 𝜓 ∧ 𝜒 ) ) ) |
| 2 |
|
nan |
⊢ ( ( 𝜑 → ¬ ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 ) ) |
| 3 |
1 2
|
bitr2i |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) → ¬ 𝜑 ) ) |