New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > rgen2w | GIF version |
Description: Generalization rule for restricted quantification. Note that x and y needn't be distinct. (Contributed by NM, 18-Jun-2014.) |
Ref | Expression |
---|---|
rgenw.1 | ⊢ φ |
Ref | Expression |
---|---|
rgen2w | ⊢ ∀x ∈ A ∀y ∈ B φ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rgenw.1 | . . 3 ⊢ φ | |
2 | 1 | rgenw 2681 | . 2 ⊢ ∀y ∈ B φ |
3 | 2 | rgenw 2681 | 1 ⊢ ∀x ∈ A ∀y ∈ B φ |
Colors of variables: wff setvar class |
Syntax hints: ∀wral 2614 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 |
This theorem depends on definitions: df-bi 177 df-ral 2619 |
This theorem is referenced by: fnmpt2i 5733 |
Copyright terms: Public domain | W3C validator |