![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > animorr | Structured version Visualization version GIF version |
Description: Conjunction implies disjunction with one common formula (2/4). (Contributed by BJ, 4-Oct-2019.) |
Ref | Expression |
---|---|
animorr | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 483 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | olcd 872 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∨ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∨ wo 845 |
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 206 df-an 395 df-or 846 |
This theorem is referenced by: nelpr2 4660 hashf1 14458 gsummoncoe1 22234 mp2pm2mplem4 22731 relogbf 26743 tgcolg 28378 colmid 28512 3vfriswmgrlem 30107 satfvsucsuc 35008 bj-dfbi6 36084 itschlc0xyqsol1 47917 |
Copyright terms: Public domain | W3C validator |