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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfa1-o | Structured version Visualization version GIF version |
Description: 𝑥 is not free in ∀𝑥𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfa1-o | ⊢ Ⅎ𝑥∀𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1-o 36027 | . 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) | |
2 | 1 | nf5i 2146 | 1 ⊢ Ⅎ𝑥∀𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1531 Ⅎwnf 1780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-10 2141 ax-c5 36013 ax-c4 36014 ax-c7 36015 |
This theorem depends on definitions: df-bi 209 df-ex 1777 df-nf 1781 |
This theorem is referenced by: axc11n-16 36068 ax12eq 36071 ax12el 36072 ax12v2-o 36079 |
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