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Mirrors > Home > ILE Home > Th. List > a5i | GIF version |
Description: Inference generalizing a consequent. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
a5i.1 | ⊢ (∀xφ → ψ) |
Ref | Expression |
---|---|
a5i | ⊢ (∀xφ → ∀xψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1430 | . . 3 ⊢ (∀xφ → ∀x∀xφ) | |
2 | ax-5 1333 | . . 3 ⊢ (∀x(∀xφ → ψ) → (∀x∀xφ → ∀xψ)) | |
3 | 1, 2 | syl5 28 | . 2 ⊢ (∀x(∀xφ → ψ) → (∀xφ → ∀xψ)) |
4 | a5i.1 | . 2 ⊢ (∀xφ → ψ) | |
5 | 3, 4 | mpg 1337 | 1 ⊢ (∀xφ → ∀xψ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1240 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-5 1333 ax-gen 1335 ax-ial 1424 |
This theorem is referenced by: hbae 1603 equveli 1639 hbsb2a 1684 hbsb2e 1685 aev 1690 dveeq2or 1694 hbsb2 1714 nfsb2or 1715 reu6 2724 |
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