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Mirrors > Home > NFE Home > Th. List > exbid | GIF version |
Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.) |
Ref | Expression |
---|---|
exbid.1 | ⊢ Ⅎxφ |
exbid.2 | ⊢ (φ → (ψ ↔ χ)) |
Ref | Expression |
---|---|
exbid | ⊢ (φ → (∃xψ ↔ ∃xχ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exbid.1 | . . 3 ⊢ Ⅎxφ | |
2 | 1 | nfri 1762 | . 2 ⊢ (φ → ∀xφ) |
3 | exbid.2 | . 2 ⊢ (φ → (ψ ↔ χ)) | |
4 | 2, 3 | exbidh 1591 | 1 ⊢ (φ → (∃xψ ↔ ∃xχ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∃wex 1541 Ⅎwnf 1544 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-nf 1545 |
This theorem is referenced by: mobid 2238 rexbida 2629 rexeqf 2804 opabbid 4624 dfid3 4768 oprabbid 5563 |
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