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Mirrors > Home > ILE Home > Th. List > sbelx | GIF version |
Description: Elimination of substitution. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sbelx | ⊢ (𝜑 ↔ ∃𝑥(𝑥 = 𝑦 ∧ [𝑥 / 𝑦]𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1536 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | sb5rf 1862 | 1 ⊢ (𝜑 ↔ ∃𝑥(𝑥 = 𝑦 ∧ [𝑥 / 𝑦]𝜑)) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 ↔ wb 105 ∃wex 1502 [wsb 1772 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-11 1516 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 |
This theorem depends on definitions: df-bi 117 df-sb 1773 |
This theorem is referenced by: sbel2x 2009 |
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