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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 1466 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | rexlimiv.1 | . 2 ⊢ (𝑥 ∈ 𝐴 → (𝜑 → 𝜓)) | |
3 | 1, 2 | rexlimi 2482 | 1 ⊢ (∃𝑥 ∈ 𝐴 𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 1438 ∃wrex 2360 |
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 1381 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-4 1445 ax-17 1464 ax-ial 1472 ax-i5r 1473 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-ral 2364 df-rex 2365 |
This theorem is referenced by: rexlimiva 2484 rexlimivw 2485 rexlimivv 2494 r19.36av 2518 r19.44av 2526 r19.45av 2527 rexn0 3378 uniss2 3682 elres 4743 ssimaex 5359 tfrlem5 6071 tfrlem8 6075 ecoptocl 6369 mapsn 6437 findcard 6594 findcard2 6595 findcard2s 6596 fiintim 6629 prnmaddl 7039 0re 7478 cnegexlem2 7648 0cnALT 7662 bndndx 8662 uzn0 9024 ublbneg 9088 rexanuz2 10412 bj-inf2vnlem2 11749 |
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