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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.) Remove dependency on ax-10 2019. (Revised by Wolf Lammen, 14-Jul-2021.) |
Ref | Expression |
---|---|
chvarv.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
chvarv.2 | ⊢ 𝜑 |
Ref | Expression |
---|---|
chvarv | ⊢ 𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chvarv.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
2 | 1 | spv 2260 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) |
3 | chvarv.2 | . 2 ⊢ 𝜑 | |
4 | 2, 3 | mpg 1724 | 1 ⊢ 𝜓 |
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