![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > stoic2b | GIF version |
Description: Stoic logic Thema 2
version b. See stoic2a 1364.
Version b is with the phrase "or both". We already have this rule as mpd3an3 1275, 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 1275 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∧ w3a 925 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 927 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |