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Mirrors > Home > MPE Home > Th. List > sbid2v | Structured version Visualization version GIF version |
Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sbid2v | ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1957 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | sbid2 2489 | 1 ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 198 [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 2055 ax-10 2135 ax-12 2163 ax-13 2334 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-ex 1824 df-nf 1828 df-sb 2012 |
This theorem is referenced by: sbelx 2537 sbco4lem 2545 |
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