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Mirrors > Home > MPE Home > Th. List > 19.16 | Structured version Visualization version GIF version |
Description: Theorem 19.16 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
19.16.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
19.16 | ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.16.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | 19.3 2195 | . 2 ⊢ (∀𝑥𝜑 ↔ 𝜑) |
3 | albi 1821 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓)) | |
4 | 2, 3 | bitr3id 285 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ ∀𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∀wal 1537 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-12 2171 |
This theorem depends on definitions: df-bi 206 df-ex 1783 df-nf 1787 |
This theorem is referenced by: (None) |
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