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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 1419 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | 1 | 19.23h 1387 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∀wal 1241 ∃wex 1381 |
This theorem was proved from axioms: ax-mp 7 ax-gen 1338 ax-ie2 1383 ax-17 1419 |
This theorem is referenced by: 19.23vv 1764 2eu4 1993 gencbval 2602 euind 2728 reuind 2744 unissb 3610 dftr2 3856 ssrelrel 4440 cotr 4706 dffun2 4912 fununi 4967 dff13 5407 acexmidlem2 5509 |
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