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Mirrors > Home > MPE Home > Th. List > sb2vOLD | Structured version Visualization version GIF version |
Description: Obsolete as of 30-Jul-2023. Use sb6 2092 instead. Version of sb2 2503 with a disjoint variable condition, which does not require ax-13 2389. (Contributed by BJ, 31-May-2019.) Revise df-sb 2069. (Revised by Steven Nguyen, 8-Jul-2023.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sb2vOLD | ⊢ (∀𝑥(𝑥 = 𝑦 → 𝜑) → [𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb6 2092 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 ↔ ∀𝑥(𝑥 = 𝑦 → 𝜑)) | |
2 | 1 | biimpri 230 | 1 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝜑) → [𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 [wsb 2068 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1780 df-sb 2069 |
This theorem is referenced by: equsb1vOLD 2112 sb6OLD 2279 sbi1vOLD 2322 |
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