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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-sbf4 | Structured version Visualization version GIF version |
Description: Substitution has no effect on a bound variabe (non-freeness case); see sbf2 2382. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-sbf4 | ⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnf1 2031 | . 2 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑 | |
2 | 1 | sbf 2380 | 1 ⊢ ([𝑦 / 𝑥]Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 Ⅎwnf 1708 [wsb 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-sb 1881 |
This theorem is referenced by: (None) |
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