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Mirrors > Home > MPE Home > Th. List > rmobii | Structured version Visualization version 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 11 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 ↔ 𝜓)) |
3 | 2 | rmobiia 3397 | 1 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥 ∈ 𝐴 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∈ wcel 2114 ∃*wrmo 3143 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-mo 2622 df-rmo 3148 |
This theorem is referenced by: 2reu5a 3737 reuxfrd 3741 brdom7disj 9955 2sqreulem4 26032 reuxfrdf 30257 cvmlift2lem13 32564 nomaxmo 33203 ineccnvmo 35613 dfeldisj5 35956 |
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