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Mirrors > Home > MPE Home > Th. List > stoic4b | Structured version Visualization version GIF version |
Description: Stoic logic Thema 4 version b. This is version b, which is with the phrase "or both". See stoic4a 1784 for more information. (Contributed by David A. Wheeler, 17-Feb-2019.) |
Ref | Expression |
---|---|
stoic4b.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
stoic4b.2 | ⊢ (((𝜒 ∧ 𝜑 ∧ 𝜓) ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
stoic4b | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stoic4b.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | 3adant3 1131 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜒) |
3 | simp1 1135 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜑) | |
4 | simp2 1136 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜓) | |
5 | simp3 1137 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜃) | |
6 | stoic4b.2 | . 2 ⊢ (((𝜒 ∧ 𝜑 ∧ 𝜓) ∧ 𝜃) → 𝜏) | |
7 | 2, 3, 4, 5, 6 | syl31anc 1372 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1086 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 397 df-3an 1088 |
This theorem is referenced by: (None) |
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