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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-sbf3 | Structured version Visualization version GIF version |
Description: Substitution has no effect on a bound variable (existential quantifier case); see sbf2 2255. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-sbf3 | ⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2139 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | 1 | sbf 2254 | 1 ⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∃wex 1773 [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-ex 1774 df-nf 1778 df-sb 2060 |
This theorem is referenced by: (None) |
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