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Mirrors > Home > NFE Home > Th. List > ralrimiv | GIF version |
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ralrimiv.1 | ⊢ (φ → (x ∈ A → ψ)) |
Ref | Expression |
---|---|
ralrimiv | ⊢ (φ → ∀x ∈ A ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . 2 ⊢ Ⅎxφ | |
2 | ralrimiv.1 | . 2 ⊢ (φ → (x ∈ A → ψ)) | |
3 | 1, 2 | ralrimi 2695 | 1 ⊢ (φ → ∀x ∈ A ψ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1710 ∀wral 2614 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 df-ral 2619 |
This theorem is referenced by: ralrimiva 2697 ralrimivw 2698 ralrimivv 2705 r19.27av 2752 rr19.3v 2980 rabssdv 3346 rzal 3651 pw1disj 4167 nnadjoin 4520 fmpt2d 5695 nnc3n3p1 6278 |
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