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Metamath Proof Explorer
Description: Stoic logic Thema 1 (part b). The other part of thema 1 of Stoic logic;
see stoic1a . (Contributed by David A. Wheeler, 16-Feb-2019)
|
|
Ref |
Expression |
|
Hypothesis |
stoic1.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) |
|
Assertion |
stoic1b |
⊢ ( ( 𝜓 ∧ ¬ 𝜃 ) → ¬ 𝜑 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
stoic1.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 ) |
| 2 |
1
|
ancoms |
⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜃 ) |
| 3 |
2
|
stoic1a |
⊢ ( ( 𝜓 ∧ ¬ 𝜃 ) → ¬ 𝜑 ) |