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Mirrors > Home > NFE Home > Th. List > 19.21bbi | GIF version |
Description: Inference removing double quantifier. (Contributed by NM, 20-Apr-1994.) |
Ref | Expression |
---|---|
19.21bbi.1 | ⊢ (φ → ∀x∀yψ) |
Ref | Expression |
---|---|
19.21bbi | ⊢ (φ → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.21bbi.1 | . . 3 ⊢ (φ → ∀x∀yψ) | |
2 | 1 | 19.21bi 1758 | . 2 ⊢ (φ → ∀yψ) |
3 | 2 | 19.21bi 1758 | 1 ⊢ (φ → ψ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 |
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 |
This theorem is referenced by: ssfin 4470 funun 5146 fnfrec 6320 |
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