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Mirrors > Home > MPE Home > Th. List > nfs1f | Structured version Visualization version GIF version |
Description: If 𝑥 is not free in 𝜑, it is not free in [𝑦 / 𝑥]𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfs1f.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfs1f | ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfs1f.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | sbf 2234 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑) |
3 | 2, 1 | nfxfr 1834 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1765 [wsb 2042 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1777 ax-4 1791 ax-5 1888 ax-6 1947 ax-7 1992 ax-12 2141 |
This theorem depends on definitions: df-bi 208 df-ex 1762 df-nf 1766 df-sb 2043 |
This theorem is referenced by: (None) |
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