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Mirrors > Home > ILE Home > Th. List > eximdv | GIF version |
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-1994.) |
Ref | Expression |
---|---|
alimdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
eximdv | ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1459 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | alimdv.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | eximdh 1542 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: 2eximdv 1803 reximdv2 2460 cgsexg 2634 spc3egv 2689 euind 2779 ssel 2993 reupick 3248 reximdva0m 3263 uniss 3622 eusvnfb 4204 coss1 4509 coss2 4510 dmss 4552 dmcosseq 4621 funssres 4962 imain 5001 brprcneu 5191 fv3 5218 dffo4 5336 dffo5 5337 f1eqcocnv 5451 dmaddpq 6569 dmmulpq 6570 recexprlemlol 6816 recexprlemupu 6818 ioom 9269 |
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