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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 2062. (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 2070 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 Ⅎwnf 1699 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nf 1701 |
This theorem is referenced by: moexex 2529 ralrimd 2942 pssnn 8063 fiint 8122 wl-mo3t 32537 pm14.24 37655 |
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