![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > simp13 | GIF version |
Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011.) |
Ref | Expression |
---|---|
simp13 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 999 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒) | |
2 | 1 | 3ad2ant1 1018 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 978 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-3an 980 |
This theorem is referenced by: simpl13 1074 simpr13 1083 simp113 1128 simp213 1137 simp313 1146 funtpg 5262 dvdsgcd 11983 coprimeprodsq 12227 pythagtriplem4 12238 pythagtriplem13 12246 pythagtriplem14 12247 pythagtriplem16 12249 pythagtrip 12253 |
Copyright terms: Public domain | W3C validator |