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Mirrors > Home > MPE Home > Th. List > animorrl | Structured version Visualization version GIF version |
Description: Conjunction implies disjunction with one common formula (4/4). (Contributed by BJ, 4-Oct-2019.) |
Ref | Expression |
---|---|
animorrl | ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 488 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | orcd 870 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 ∨ 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∨ wo 844 |
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 210 df-an 400 df-or 845 |
This theorem is referenced by: nelpr1 4553 ccatsymb 13927 sadadd2lem2 15789 mreexexlem4d 16910 drngnidl 19995 ppttop 21612 wilthlem2 25654 bcmono 25861 addsqnreup 26027 mideulem2 26528 linds2eq 30995 fnwe2lem3 39996 disjxp1 41703 nnfoctbdjlem 43094 |
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