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Mirrors > Home > MPE Home > Th. List > 19.28v | Structured version Visualization version GIF version |
Description: Version of 19.28 2217 with a disjoint variable condition, requiring fewer axioms. (Contributed by NM, 25-Mar-2004.) |
Ref | Expression |
---|---|
19.28v | ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1866 | . 2 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓)) | |
2 | 19.3v 1978 | . 2 ⊢ (∀𝑥𝜑 ↔ 𝜑) | |
3 | 1, 2 | bianbi 625 | 1 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 394 ∀wal 1532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 |
This theorem depends on definitions: df-bi 206 df-an 395 df-ex 1775 |
This theorem is referenced by: reu6 3720 dfer2 8735 kmlem14 10206 kmlem15 10207 bnj1176 34850 bnj1186 34852 ismnuprim 43968 19.28vv 44060 |
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