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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 variabe (existential quantifier case); see sbf2 2457. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-sbf3 | ⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2143 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | 1 | sbf 2455 | 1 ⊢ ([𝑦 / 𝑥]∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 ∃wex 1823 [wsb 2011 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2054 ax-10 2134 ax-12 2162 ax-13 2333 |
This theorem depends on definitions: df-bi 199 df-an 387 df-ex 1824 df-nf 1828 df-sb 2012 |
This theorem is referenced by: (None) |
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