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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ssbid2 | Structured version Visualization version GIF version |
Description: A special case of sbequ2 2240. (Contributed by BJ, 22-Dec-2020.) |
Ref | Expression |
---|---|
bj-ssbid2 | ⊢ ([𝑥 / 𝑥]𝜑 → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 2010 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | sbequ2 2240 | . 2 ⊢ (𝑥 = 𝑥 → ([𝑥 / 𝑥]𝜑 → 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝑥 / 𝑥]𝜑 → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 2060 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-sb 2061 |
This theorem is referenced by: (None) |
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