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Mirrors > Home > MPE Home > Th. List > Mathboxes > sbidd-misc | Structured version Visualization version GIF version |
Description: An identity theorem for substitution. See sbid 2289. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.) |
Ref | Expression |
---|---|
sbidd-misc | ⊢ ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbid 2289 | . 2 ⊢ ([𝑥 / 𝑥]𝜓 ↔ 𝜓) | |
2 | 1 | imbi2i 328 | 1 ⊢ ((𝜑 → [𝑥 / 𝑥]𝜓) ↔ (𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 [wsb 2067 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-12 2220 |
This theorem depends on definitions: df-bi 199 df-an 387 df-ex 1879 df-sb 2068 |
This theorem is referenced by: (None) |
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