Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > syld3an2 | GIF version |
Description: A syllogism inference. (Contributed by NM, 20-May-2007.) |
Ref | Expression |
---|---|
syld3an2.1 | ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → 𝜓) |
syld3an2.2 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
syld3an2 | ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syld3an2.1 | . . . 4 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → 𝜓) | |
2 | 1 | 3com23 1110 | . . 3 ⊢ ((𝜑 ∧ 𝜃 ∧ 𝜒) → 𝜓) |
3 | syld3an2.2 | . . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) | |
4 | 3 | 3com23 1110 | . . 3 ⊢ ((𝜑 ∧ 𝜃 ∧ 𝜓) → 𝜏) |
5 | 2, 4 | syld3an3 1180 | . 2 ⊢ ((𝜑 ∧ 𝜃 ∧ 𝜒) → 𝜏) |
6 | 5 | 3com23 1110 | 1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ 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: nppcan2 7242 nnncan 7246 nnncan2 7248 ltdivmul 7842 ledivmul 7843 ltdiv23 7858 lediv23 7859 |
Copyright terms: Public domain | W3C validator |