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Mirrors > Home > ILE Home > Th. List > alrimdv | GIF version |
Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
alrimdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
alrimdv | ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1419 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | ax-17 1419 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
3 | alrimdv.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
4 | 1, 2, 3 | alrimdh 1368 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1241 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-5 1336 ax-gen 1338 ax-17 1419 |
This theorem is referenced by: funcnvuni 4968 fliftfun 5436 findcard 6345 findcard2 6346 findcard2s 6347 genprndl 6619 genprndu 6620 bj-inf2vnlem2 10096 |
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