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Mirrors > Home > MPE Home > Th. List > spesbcd | Structured version Visualization version GIF version |
Description: form of spsbc 3788. (Contributed by Mario Carneiro, 9-Feb-2017.) |
Ref | Expression |
---|---|
spesbcd.1 | ⊢ (𝜑 → [𝐴 / 𝑥]𝜓) |
Ref | Expression |
---|---|
spesbcd | ⊢ (𝜑 → ∃𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | spesbcd.1 | . 2 ⊢ (𝜑 → [𝐴 / 𝑥]𝜓) | |
2 | spesbc 3873 | . 2 ⊢ ([𝐴 / 𝑥]𝜓 → ∃𝑥𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1774 [wsbc 3775 |
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 2167 ax-ext 2699 |
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 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ral 3058 df-rex 3067 df-v 3472 df-sbc 3776 |
This theorem is referenced by: euotd 5509 ex-natded9.26 30222 bnj1465 34470 spesbcdi 37587 iscard4 42957 minregex 42958 brtrclfv2 43151 cotrclrcl 43166 |
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