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Mirrors > Home > ILE Home > Th. List > ralrimdv | GIF version |
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998.) |
Ref | Expression |
---|---|
ralrimdv.1 | ⊢ (𝜑 → (𝜓 → (𝑥 ∈ 𝐴 → 𝜒))) |
Ref | Expression |
---|---|
ralrimdv | ⊢ (𝜑 → (𝜓 → ∀𝑥 ∈ 𝐴 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1515 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | nfv 1515 | . 2 ⊢ Ⅎ𝑥𝜓 | |
3 | ralrimdv.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝑥 ∈ 𝐴 → 𝜒))) | |
4 | 1, 2, 3 | ralrimd 2542 | 1 ⊢ (𝜑 → (𝜓 → ∀𝑥 ∈ 𝐴 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2135 ∀wral 2442 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-4 1497 ax-17 1513 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-ral 2447 |
This theorem is referenced by: ralrimdva 2544 ralrimivv 2545 nneneq 6814 fzrevral 10030 topbas 12614 neipsm 12701 cnpnei 12766 metcnp3 13058 |
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