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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nnfth | Structured version Visualization version GIF version |
Description: A variable is nonfree in a theorem, inference form. (Contributed by BJ, 28-Jul-2023.) |
Ref | Expression |
---|---|
bj-nnfth.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
bj-nnfth | ⊢ Ⅎ'𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnfth.1 | . 2 ⊢ 𝜑 | |
2 | bj-nnftht 34931 | . 2 ⊢ ((𝜑 ∧ ∀𝑥𝜑) → Ⅎ'𝑥𝜑) | |
3 | 1, 2 | bj-mpgs 34799 | 1 ⊢ Ⅎ'𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎ'wnnf 34913 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 |
This theorem depends on definitions: df-bi 206 df-an 397 df-bj-nnf 34914 |
This theorem is referenced by: bj-nnfnth 34933 |
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