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Mirrors > Home > NFE Home > Th. List > ceqsexv | GIF version |
Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995.) |
Ref | Expression |
---|---|
ceqsexv.1 | ⊢ A ∈ V |
ceqsexv.2 | ⊢ (x = A → (φ ↔ ψ)) |
Ref | Expression |
---|---|
ceqsexv | ⊢ (∃x(x = A ∧ φ) ↔ ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . 2 ⊢ Ⅎxψ | |
2 | ceqsexv.1 | . 2 ⊢ A ∈ V | |
3 | ceqsexv.2 | . 2 ⊢ (x = A → (φ ↔ ψ)) | |
4 | 1, 2, 3 | ceqsex 2893 | 1 ⊢ (∃x(x = A ∧ φ) ↔ ψ) |
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