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Mirrors > Home > ILE Home > Th. List > stoic2b | GIF version |
Description: Stoic logic Thema 2
version b. See stoic2a 1318.
Version b is with the phrase "or both". We already have this rule as mpd3an3 1233, 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 1233 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∧ w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: (None) |
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