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Mirrors > Home > ILE Home > Th. List > alimdh | GIF version |
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 4-Jan-2002.) |
Ref | Expression |
---|---|
alimdh.1 | ⊢ (φ → ∀xφ) |
alimdh.2 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
alimdh | ⊢ (φ → (∀xψ → ∀xχ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alimdh.1 | . 2 ⊢ (φ → ∀xφ) | |
2 | alimdh.2 | . . 3 ⊢ (φ → (ψ → χ)) | |
3 | 2 | al2imi 1344 | . 2 ⊢ (∀xφ → (∀xψ → ∀xχ)) |
4 | 1, 3 | syl 14 | 1 ⊢ (φ → (∀xψ → ∀xχ)) |
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 |
This theorem is referenced by: alrimdh 1365 hbald 1377 alimd 1411 hbimd 1462 dral1 1615 sbiedh 1667 ax16 1691 ax16i 1735 alimdv 1756 |
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