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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 1604 | . 2 ⊢ (∃𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (∀𝑥𝜑 → ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1330 ∃wex 1469 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: 19.36i 1651 spimed 1719 |
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