Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-notalbii | Structured version Visualization version GIF version |
Description: Equivalence of universal quantification of negation of equivalent formulas. Shortens ab0 3905, ballotlem2 29877, bnj1143 30115, hausdiag 21258. (Contributed by BJ, 17-Jul-2021.) |
Ref | Expression |
---|---|
bj-notalbii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
bj-notalbii | ⊢ (∀𝑥 ¬ 𝜑 ↔ ∀𝑥 ¬ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-notalbii.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
2 | 1 | notbii 309 | . 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜓) |
3 | 2 | albii 1737 | 1 ⊢ (∀𝑥 ¬ 𝜑 ↔ ∀𝑥 ¬ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |