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Mirrors > Home > ILE Home > Th. List > rmobii | GIF version |
Description: Formula-building rule for restricted existential quantifier (inference form). (Contributed by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
rmobii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
rmobii | ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rmobii.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
2 | 1 | a1i 9 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ↔ 𝜓)) |
3 | 2 | rmobiia 2597 | 1 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∈ wcel 1465 ∃*wrmo 2396 |
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 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-eu 1980 df-mo 1981 df-rmo 2401 |
This theorem is referenced by: infmoti 6883 |
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