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Mirrors > Home > MPE Home > Th. List > sbid2vw | Structured version Visualization version GIF version |
Description: Reverting substitution yields the original expression. Based on fewer axioms than sbid2v 2512, at the expense of an extra distinct variable condition. (Contributed by NM, 14-May-1993.) (Revised by Wolf Lammen, 5-Aug-2023.) |
Ref | Expression |
---|---|
sbid2vw | ⊢ ([𝑡 / 𝑥][𝑥 / 𝑡]𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbequ12r 2250 | . 2 ⊢ (𝑥 = 𝑡 → ([𝑥 / 𝑡]𝜑 ↔ 𝜑)) | |
2 | 1 | sbievw 2091 | 1 ⊢ ([𝑡 / 𝑥][𝑥 / 𝑡]𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 206 [wsb 2062 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-12 2175 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1777 df-sb 2063 |
This theorem is referenced by: sbco4lemOLDOLD 2277 ichid 47376 |
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