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| Mirrors > Home > MPE Home > Th. List > alrimd | Structured version Visualization version GIF version | ||
| Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2207. (Contributed by Mario Carneiro, 24-Sep-2016.) | 
| Ref | Expression | 
|---|---|
| alrimd.1 | ⊢ Ⅎ𝑥𝜑 | 
| alrimd.2 | ⊢ Ⅎ𝑥𝜓 | 
| alrimd.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) | 
| Ref | Expression | 
|---|---|
| alrimd | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | alrimd.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
| 2 | alrimd.2 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
| 3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → Ⅎ𝑥𝜓) | 
| 4 | alrimd.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
| 5 | 1, 3, 4 | alrimdd 2214 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∀wal 1538 Ⅎwnf 1783 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 | 
| This theorem depends on definitions: df-bi 207 df-ex 1780 df-nf 1784 | 
| This theorem is referenced by: moexexlem 2626 ralrimd 3264 pssnn 9208 fiint 9366 fiintOLD 9367 wl-mo3t 37577 pm14.24 44451 | 
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