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Metamath Proof Explorer
Description: Conjunction with implication. Compare Theorem *4.45 of WhiteheadRussell
p. 119. (Contributed by NM, 17-May-1998)
|
|
Ref |
Expression |
|
Assertion |
pm4.45im |
⊢ ( 𝜑 ↔ ( 𝜑 ∧ ( 𝜓 → 𝜑 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ax-1 |
⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) ) |
| 2 |
1
|
pm4.71i |
⊢ ( 𝜑 ↔ ( 𝜑 ∧ ( 𝜓 → 𝜑 ) ) ) |