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Mirrors > Home > MPE Home > Th. List > Mathboxes > 19.28vv | Structured version Visualization version GIF version |
Description: Theorem *11.47 in [WhiteheadRussell] p. 164. Theorem 19.28 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.) |
Ref | Expression |
---|---|
19.28vv | ⊢ (∀𝑥∀𝑦(𝜓 ∧ 𝜑) ↔ (𝜓 ∧ ∀𝑥∀𝑦𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.28v 2000 | . . 3 ⊢ (∀𝑦(𝜓 ∧ 𝜑) ↔ (𝜓 ∧ ∀𝑦𝜑)) | |
2 | 1 | albii 1827 | . 2 ⊢ (∀𝑥∀𝑦(𝜓 ∧ 𝜑) ↔ ∀𝑥(𝜓 ∧ ∀𝑦𝜑)) |
3 | 19.28v 2000 | . 2 ⊢ (∀𝑥(𝜓 ∧ ∀𝑦𝜑) ↔ (𝜓 ∧ ∀𝑥∀𝑦𝜑)) | |
4 | 2, 3 | bitri 278 | 1 ⊢ (∀𝑥∀𝑦(𝜓 ∧ 𝜑) ↔ (𝜓 ∧ ∀𝑥∀𝑦𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ∧ wa 399 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 |
This theorem is referenced by: (None) |
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