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Mirrors > Home > MPE Home > Th. List > nfimt2 | Structured version Visualization version GIF version |
Description: Closed form of nfim 1825 and uncurried (imported) form of nfimt 1821. (Contributed by BJ, 20-Oct-2021.) |
Ref | Expression |
---|---|
nfimt2 | ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfimt 1821 | . 2 ⊢ (Ⅎ𝑥𝜑 → (Ⅎ𝑥𝜓 → Ⅎ𝑥(𝜑 → 𝜓))) | |
2 | 1 | imp 445 | 1 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 Ⅎwnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-nf 1710 |
This theorem is referenced by: nfimd 1823 nfim 1825 |
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