![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > simp-8r | Structured version Visualization version GIF version |
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) (Proof shortened by Wolf Lammen, 24-May-2022.) |
Ref | Expression |
---|---|
simp-8r | ⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 471 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | ad7antr 724 | 1 ⊢ (((((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜁) ∧ 𝜎) ∧ 𝜌) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 382 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 383 |
This theorem is referenced by: simp-9rOLD 791 legso 25715 opphl 25867 f1otrg 25972 2sqmo 29989 qtophaus 30243 esumcst 30465 smfmullem3 41517 |
Copyright terms: Public domain | W3C validator |