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Mirrors > Home > MPE Home > Th. List > stoic2b | Structured version Visualization version GIF version |
Description: Stoic logic Thema 2 version b. See stoic2a 1776. Version b is with the phrase "or both". We already have this rule as mpd3an3 1459, so here we prove the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.) |
Ref | Expression |
---|---|
stoic2b.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
stoic2b.2 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
stoic2b | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | stoic2b.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | stoic2b.2 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | mpd3an3 1459 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1084 |
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 210 df-an 400 df-3an 1086 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |