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| Mirrors > Home > MPE Home > Th. List > Mathboxes > jabtaib | Structured version Visualization version GIF version | ||
| Description: For when pm3.4 lacks a pm3.4i. (Contributed by Jarvin Udandy, 9-Sep-2020.) | 
| Ref | Expression | 
|---|---|
| jabtaib.1 | ⊢ (𝜑 ∧ 𝜓) | 
| Ref | Expression | 
|---|---|
| jabtaib | ⊢ (𝜑 → 𝜓) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | jabtaib.1 | . 2 ⊢ (𝜑 ∧ 𝜓) | |
| 2 | pm3.4 810 | . 2 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 → 𝜓)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → 𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 | 
| 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 207 df-an 396 | 
| This theorem is referenced by: (None) | 
| Copyright terms: Public domain | W3C validator |