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Mirrors > Home > ILE Home > Th. List > stoic1b | GIF version |
Description: Stoic logic Thema 1 (part b). The other part of thema 1 of Stoic logic; see stoic1a 1427. (Contributed by David A. Wheeler, 16-Feb-2019.) |
Ref | Expression |
---|---|
stoic1.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Ref | Expression |
---|---|
stoic1b | ⊢ ((𝜓 ∧ ¬ 𝜃) → ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stoic1.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) | |
2 | 1 | ancoms 268 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜃) |
3 | 2 | stoic1a 1427 | 1 ⊢ ((𝜓 ∧ ¬ 𝜃) → ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 |
This theorem is referenced by: (None) |
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