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| Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 2377. See sbid2vw 2259 for a version with an extra disjoint variable condition requiring fewer axioms. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| sbid2v | ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ 𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nfv 1914 | . 2 ⊢ Ⅎ𝑥𝜑 | |
| 2 | 1 | sbid2 2513 | 1 ⊢ ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑 ↔ 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-10 2141 ax-12 2177 ax-13 2377 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-ex 1780 df-nf 1784 df-sb 2065 | 
| This theorem is referenced by: (None) | 
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