![]() |
Mathbox for Giovanni Mascellani |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > spesbcdi | Structured version Visualization version GIF version |
Description: A lemma for introducing an existential quantifier, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.) |
Ref | Expression |
---|---|
spesbcdi.1 | ⊢ (𝜑 → 𝜓) |
spesbcdi.2 | ⊢ ([𝐴 / 𝑥]𝜒 ↔ 𝜓) |
Ref | Expression |
---|---|
spesbcdi | ⊢ (𝜑 → ∃𝑥𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spesbcdi.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | spesbcdi.2 | . . 3 ⊢ ([𝐴 / 𝑥]𝜒 ↔ 𝜓) | |
3 | 1, 2 | sylibr 233 | . 2 ⊢ (𝜑 → [𝐴 / 𝑥]𝜒) |
4 | 3 | spesbcd 3873 | 1 ⊢ (𝜑 → ∃𝑥𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∃wex 1774 [wsbc 3774 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2164 ax-ext 2698 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-tru 1537 df-ex 1775 df-nf 1779 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-nfc 2880 df-ral 3057 df-rex 3066 df-v 3471 df-sbc 3775 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |