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Mirrors > Home > MPE Home > Th. List > Mathboxes > sbidd | Structured version Visualization version GIF version |
Description: An identity theorem for substitution. See sbid 2100. See Remark 9.1 in [Megill] p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017.) |
Ref | Expression |
---|---|
sbidd.1 | ⊢ (𝜑 → [𝑥 / 𝑥]𝜓) |
Ref | Expression |
---|---|
sbidd | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbidd.1 | . 2 ⊢ (𝜑 → [𝑥 / 𝑥]𝜓) | |
2 | sbid 2100 | . 2 ⊢ ([𝑥 / 𝑥]𝜓 ↔ 𝜓) | |
3 | 1, 2 | sylib 207 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wsb 1867 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 df-sb 1868 |
This theorem is referenced by: (None) |
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