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Metamath Proof Explorer
Description: Join antecedents with conjunction. Theorem *3.21 of WhiteheadRussell
p. 111. (Contributed by NM, 5-Aug-1993)
|
|
Ref |
Expression |
|
Assertion |
pm3.21 |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜓 ∧ 𝜑 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
id |
⊢ ( ( 𝜓 ∧ 𝜑 ) → ( 𝜓 ∧ 𝜑 ) ) |
| 2 |
1
|
expcom |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜓 ∧ 𝜑 ) ) ) |