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Mirrors > Home > MPE Home > Th. List > spesbcd | Structured version Visualization version GIF version |
Description: form of spsbc 3784. (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 3864 | . 2 ⊢ ([𝐴 / 𝑥]𝜓 → ∃𝑥𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1776 [wsbc 3771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-v 3496 df-sbc 3772 |
This theorem is referenced by: euotd 5402 ex-natded9.26 28197 bnj1465 32117 spesbcdi 35397 iscard4 39898 brtrclfv2 40070 cotrclrcl 40085 |
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