New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > ralimdva | GIF version |
Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 22-May-1999.) |
Ref | Expression |
---|---|
ralimdva.1 | ⊢ ((φ ∧ x ∈ A) → (ψ → χ)) |
Ref | Expression |
---|---|
ralimdva | ⊢ (φ → (∀x ∈ A ψ → ∀x ∈ A χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . 2 ⊢ Ⅎxφ | |
2 | ralimdva.1 | . 2 ⊢ ((φ ∧ x ∈ A) → (ψ → χ)) | |
3 | 1, 2 | ralimdaa 2691 | 1 ⊢ (φ → (∀x ∈ A ψ → ∀x ∈ A χ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 ∈ 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-an 360 df-ex 1542 df-nf 1545 df-ral 2619 |
This theorem is referenced by: ralimdv 2693 weds 5938 nclenn 6249 spacind 6287 |
Copyright terms: Public domain | W3C validator |