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| Mirrors > Home > MPE Home > Th. List > sbcovOLD | Structured version Visualization version GIF version | ||
| Description: Obsolete version of sbcov 2256 as of 26-Aug-2025. (Contributed by NM, 14-May-1993.) (Revised by GG, 7-Aug-2023.) (Proof modification is discouraged.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| sbcovOLD | ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ [𝑦 / 𝑥]𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbcom3vv 2097 | . 2 ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ [𝑦 / 𝑥][𝑦 / 𝑦]𝜑) | |
| 2 | sbid 2255 | . . 3 ⊢ ([𝑦 / 𝑦]𝜑 ↔ 𝜑) | |
| 3 | 2 | sbbii 2076 | . 2 ⊢ ([𝑦 / 𝑥][𝑦 / 𝑦]𝜑 ↔ [𝑦 / 𝑥]𝜑) |
| 4 | 1, 3 | bitri 275 | 1 ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ [𝑦 / 𝑥]𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 [wsb 2064 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 |
| This theorem is referenced by: (None) |
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