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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-nfs1v | Structured version Visualization version GIF version |
Description: Version of nfsb2 2476 with a disjoint variable condition, which does not require ax-13 2365, and removal of ax-13 2365 from nfs1v 2145. (Contributed by BJ, 24-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nfs1v | ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-hbs1 36198 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) | |
2 | 1 | nf5i 2134 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1777 [wsb 2059 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-10 2129 ax-12 2163 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-ex 1774 df-nf 1778 df-sb 2060 |
This theorem is referenced by: (None) |
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