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Metamath Proof Explorer
Description: Distribution of implication with conjunction (deduction version with
conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011)
|
|
Ref |
Expression |
|
Hypothesis |
imdistanda.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) ) |
|
Assertion |
imdistanda |
⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
imdistanda.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) ) |
| 2 |
1
|
ex |
⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) |
| 3 |
2
|
imdistand |
⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) ) ) |