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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-jaoi1 | Structured version Visualization version GIF version |
Description: Shortens orfa2 35930 (58>53), pm1.2 904 (20>18), pm1.2 904 (20>18), pm2.4 907 (31>25), pm2.41 908 (31>25), pm2.42 943 (38>32), pm3.2ni 881 (43>39), pm4.44 997 (55>51). (Contributed by BJ, 30-Sep-2019.) |
Ref | Expression |
---|---|
bj-jaoi1.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
bj-jaoi1 | ⊢ ((𝜑 ∨ 𝜓) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-jaoi1.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | id 22 | . 2 ⊢ (𝜓 → 𝜓) | |
3 | 1, 2 | jaoi 857 | 1 ⊢ ((𝜑 ∨ 𝜓) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 847 |
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-or 848 |
This theorem is referenced by: bj-falor2 34453 bj-prmoore 34970 |
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