![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > alrimih | Structured version Visualization version GIF version |
Description: Inference form of Theorem 19.21 of [Margaris] p. 90. See 19.21 2200 and 19.21h 2283. Instance of sylg 1825. (Contributed by NM, 9-Jan-1993.) (Revised by BJ, 31-Mar-2021.) |
Ref | Expression |
---|---|
alrimih.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
alrimih.2 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
alrimih | ⊢ (𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimih.1 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | alrimih.2 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | sylg 1825 | 1 ⊢ (𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1539 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-gen 1797 ax-4 1811 |
This theorem is referenced by: nexdh 1868 albidh 1869 alrimiv 1930 ax12i 1970 cbvaliw 2009 nf5dh 2143 alrimi 2206 hbnd 2292 cbv3v 2331 cbv3 2396 eujustALT 2566 axi5r 2695 hbralrimi 3144 ralidmw 4507 bnj1093 34060 bj-abvALT 35873 bj-gabssd 35902 mpobi123f 37116 axc4i-o 37854 equidq 37880 aev-o 37887 ax12f 37896 axc5c4c711 43242 hbimpg 43397 gen11nv 43460 |
Copyright terms: Public domain | W3C validator |