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Mirrors > Home > ILE Home > Th. List > r19.23v | GIF version |
Description: Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 31-Aug-1999.) |
Ref | Expression |
---|---|
r19.23v | ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) ↔ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | 1 | r19.23 2517 | 1 ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) ↔ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 104 ∀wral 2393 ∃wrex 2394 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-ral 2398 df-rex 2399 |
This theorem is referenced by: uniiunlem 3155 dfiin2g 3816 iunss 3824 ralxfr2d 4355 rexxfr2d 4356 ssrel2 4599 reliun 4630 funimaexglem 5176 funimass4 5440 ralrnmpo 5853 |
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