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| Mirrors > Home > ILE Home > Th. List > 19.23v | GIF version | ||
| Description: Special case of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jun-1998.) |
| Ref | Expression |
|---|---|
| 19.23v | ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-17 1540 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
| 2 | 1 | 19.23h 1512 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
| Colors of variables: wff set class |
| Syntax hints: → wi 4 ↔ wb 105 ∀wal 1362 ∃wex 1506 |
| This theorem was proved from axioms: ax-mp 5 ax-gen 1463 ax-ie2 1508 ax-17 1540 |
| This theorem is referenced by: 19.23vv 1898 2eu4 2138 gencbval 2812 euind 2951 reuind 2969 snssb 3755 unissb 3869 disjnim 4024 dftr2 4133 ssrelrel 4763 cotr 5051 dffun2 5268 fununi 5326 dff13 5815 acexmidlem2 5919 |
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