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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 4650 hashf1 14471 gsummoncoe1 22296 mp2pm2mplem4 22799 relogbf 26816 tgcolg 28478 colmid 28612 3vfriswmgrlem 30207 satfvsucsuc 35206 bj-dfbi6 36292 itschlc0xyqsol1 48190 |
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