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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ssbid1 | Structured version Visualization version GIF version |
Description: A special case of sbequ1 2249. (Contributed by BJ, 22-Dec-2020.) |
Ref | Expression |
---|---|
bj-ssbid1 | ⊢ (𝜑 → [𝑥 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2019 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | sbequ1 2249 | . 2 ⊢ (𝑥 = 𝑥 → (𝜑 → [𝑥 / 𝑥]𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → [𝑥 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 2069 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-sb 2070 |
This theorem is referenced by: (None) |
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