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Mirrors > Home > ILE Home > Th. List > rmobii | GIF version |
Description: Formula-building rule for restricted existential quantifier (inference rule). (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 2543 | 1 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 103 ∈ wcel 1433 ∃*wrmo 2351 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-eu 1944 df-mo 1945 df-rmo 2356 |
This theorem is referenced by: infmoti 6441 |
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