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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnfv | Structured version Visualization version GIF version |
Description: A non-occurring variable is nonfree in a formula. (Contributed by BJ, 28-Jul-2023.) |
Ref | Expression |
---|---|
bj-nnfv | ⊢ Ⅎ'𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax5e 1912 | . 2 ⊢ (∃𝑥𝜑 → 𝜑) | |
2 | ax-5 1910 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
3 | df-bj-nnf 34075 | . 2 ⊢ (Ⅎ'𝑥𝜑 ↔ ((∃𝑥𝜑 → 𝜑) ∧ (𝜑 → ∀𝑥𝜑))) | |
4 | 1, 2, 3 | mpbir2an 709 | 1 ⊢ Ⅎ'𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 ∃wex 1779 Ⅎ'wnnf 34074 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-5 1910 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1780 df-bj-nnf 34075 |
This theorem is referenced by: (None) |
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