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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 1506 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) | |
2 | 1 | 19.23h 1474 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) ↔ (∃𝑥𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 ∀wal 1329 ∃wex 1468 |
This theorem was proved from axioms: ax-mp 5 ax-gen 1425 ax-ie2 1470 ax-17 1506 |
This theorem is referenced by: 19.23vv 1856 2eu4 2090 gencbval 2729 euind 2866 reuind 2884 unissb 3761 disjnim 3915 dftr2 4023 ssrelrel 4634 cotr 4915 dffun2 5128 fununi 5186 dff13 5662 acexmidlem2 5764 |
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