![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > simp-4l | GIF version |
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
simp-4l | ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simplll 533 | . 2 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜑) | |
2 | 1 | adantr 276 | 1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
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 is referenced by: simp-5l 543 disjiun 4013 fnfi 6966 nninfisol 7161 sumeq2 11399 zsumdc 11424 modfsummod 11498 prodeq2 11597 zproddc 11619 mulgval 13064 cncnp 14190 fsumcncntop 14516 logbgcd1irrap 14848 |
Copyright terms: Public domain | W3C validator |