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Mirrors > Home > ILE Home > Th. List > 19.9v | GIF version |
Description: Special case of Theorem 19.9 of [Margaris] p. 89. (Contributed by NM, 28-May-1995.) (Revised by NM, 21-May-2007.) |
Ref | Expression |
---|---|
19.9v | ⊢ (∃𝑥𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1507 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | 19.9h 1623 | 1 ⊢ (∃𝑥𝜑 ↔ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∃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-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: spc2gv 2780 spc3gv 2782 mo2icl 2867 brtpos2 6156 |
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