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Mirrors > Home > NFE Home > Th. List > rspec | GIF version |
Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.) |
Ref | Expression |
---|---|
rspec.1 | ⊢ ∀x ∈ A φ |
Ref | Expression |
---|---|
rspec | ⊢ (x ∈ A → φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspec.1 | . 2 ⊢ ∀x ∈ A φ | |
2 | rsp 2674 | . 2 ⊢ (∀x ∈ A φ → (x ∈ A → φ)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (x ∈ A → φ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1710 ∀wral 2614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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-ral 2619 |
This theorem is referenced by: rspec2 2713 vtoclri 2929 |
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