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Mirrors > Home > ILE Home > Th. List > 19.35i | GIF version |
Description: Inference from Theorem 19.35 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.) |
Ref | Expression |
---|---|
19.35i.1 | ⊢ ∃x(φ → ψ) |
Ref | Expression |
---|---|
19.35i | ⊢ (∀xφ → ∃xψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.35i.1 | . 2 ⊢ ∃x(φ → ψ) | |
2 | 19.35-1 1512 | . 2 ⊢ (∃x(φ → ψ) → (∀xφ → ∃xψ)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (∀xφ → ∃xψ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1240 ∃wex 1378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: 19.36i 1559 spimed 1625 |
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