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Mirrors > Home > ILE Home > Th. List > rexlimiv | GIF version |
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994.) |
Ref | Expression |
---|---|
rexlimiv.1 | ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
rexlimiv | ⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | rexlimiv.1 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓)) | |
3 | 1, 2 | rexlimi 2519 | 1 ⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓) |
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: rexlimiva 2521 rexlimivw 2522 rexlimivv 2532 r19.36av 2559 r19.44av 2567 r19.45av 2568 rexn0 3431 uniss2 3737 elres 4825 ssimaex 5450 tfrlem5 6179 tfrlem8 6183 ecoptocl 6484 mapsn 6552 elixpsn 6597 ixpsnf1o 6598 findcard 6750 findcard2 6751 findcard2s 6752 fiintim 6785 prnmaddl 7266 0re 7734 cnegexlem2 7906 0cnALT 7920 bndndx 8944 uzn0 9309 ublbneg 9373 rexanuz2 10731 opnneiid 12260 bj-inf2vnlem2 13096 |
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