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Mirrors > Home > ILE Home > Th. List > rexlimdvw | GIF version |
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Jun-2014.) |
Ref | Expression |
---|---|
rexlimdvw.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
rexlimdvw | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexlimdvw.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | a1d 22 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) |
3 | 2 | rexlimdv 2525 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1465 ∃wrex 2394 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-ral 2398 df-rex 2399 |
This theorem is referenced by: nnpredcl 4506 qsss 6456 fodjuomnilemdc 6984 ltpopr 7371 ltsopr 7372 ltexprlemlol 7378 ltexprlemupu 7380 cauappcvgprlemrnd 7426 caucvgprlemrnd 7449 caucvgprprlemrnd 7477 suplocexprlemss 7491 suplocexprlemrl 7493 suplocsrlempr 7583 climuni 11030 cncnp2m 12327 bj-findis 13104 |
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