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Metamath Proof Explorer
Description: Antecedent absorption implication. Theorem *5.4 of WhiteheadRussell
p. 125. (Contributed by NM, 5-Aug-1993)
|
|
Ref |
Expression |
|
Assertion |
pm5.4 |
⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) ↔ ( 𝜑 → 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
pm5.5 |
⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) ↔ 𝜓 ) ) |
| 2 |
1
|
pm5.74i |
⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) ↔ ( 𝜑 → 𝜓 ) ) |