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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 108 | . 2 ⊢ (x ∈ A → (φ → ψ)) |
3 | 2 | rexlimiv 2421 | 1 ⊢ (∃x ∈ A φ → ψ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∈ wcel 1390 ∃wrex 2301 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-17 1416 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-ral 2305 df-rex 2306 |
This theorem is referenced by: unon 4202 ssfiexmid 6254 dmaddpqlem 6361 nqpi 6362 nq0nn 6425 recexprlemm 6596 bj-nn0suc 9424 bj-nn0sucALT 9438 |
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