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Mirrors > Home > ILE Home > Th. List > rexlimiva | GIF version |
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006.) |
Ref | Expression |
---|---|
rexlimiva.1 | ⊢ ((𝑥 ∈ 𝐴 ∧ 𝜑) → 𝜓) |
Ref | Expression |
---|---|
rexlimiva | ⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexlimiva.1 | . . 3 ⊢ ((𝑥 ∈ 𝐴 ∧ 𝜑) → 𝜓) | |
2 | 1 | ex 114 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓)) |
3 | 2 | rexlimiv 2520 | 1 ⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∈ 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: unon 4397 reg2exmidlema 4419 ssfilem 6737 diffitest 6749 fival 6826 elfi2 6828 fi0 6831 djuss 6923 updjud 6935 enumct 6968 finnum 7007 dmaddpqlem 7153 nqpi 7154 nq0nn 7218 recexprlemm 7400 rexanuz 10728 r19.2uz 10733 maxleast 10953 fsum2dlemstep 11171 fisumcom2 11175 0dvds 11440 even2n 11498 m1expe 11523 m1exp1 11525 epttop 12186 neipsm 12250 tgioo 12642 sin0pilem2 12790 pilem3 12791 bj-nn0suc 13089 bj-nn0sucALT 13103 |
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