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Mirrors > Home > ILE Home > Th. List > alimdv | GIF version |
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 3-Apr-1994.) |
Ref | Expression |
---|---|
alimdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
alimdv | ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1459 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | alimdv.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | alimdh 1396 | 1 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1282 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-5 1376 ax-gen 1378 ax-17 1459 |
This theorem is referenced by: 2alimdv 1802 moim 2005 ralimdv2 2431 sstr2 3006 reuss2 3244 ssuni 3623 disjss2 3769 disjss1 3772 soss 4069 alxfr 4211 ssrel 4446 ssrel2 4448 ssrelrel 4458 iotaval 4898 |
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