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Mirrors > Home > MPE Home > Th. List > chvarv | Structured version Visualization version GIF version |
Description: Implicit substitution of 𝑦 for 𝑥 into a theorem. (Contributed by NM, 20-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) |
Ref | Expression |
---|---|
chvarv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
chvarv.2 | ⊢ 𝜑 |
Ref | Expression |
---|---|
chvarv | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1906 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | chvarv.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
3 | chvarv.2 | . 2 ⊢ 𝜑 | |
4 | 1, 2, 3 | chvar 2404 | 1 ⊢ 𝜓 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 207 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-12 2167 ax-13 2381 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-nf 1776 |
This theorem is referenced by: bnj1326 32195 vonioo 42841 vonicc 42844 |
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