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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 1957 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | chvarv.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
3 | chvarv.2 | . 2 ⊢ 𝜑 | |
4 | 1, 2, 3 | chvar 2360 | 1 ⊢ 𝜓 |
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