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Mirrors > Home > ILE Home > Th. List > rexlimivw | GIF version |
Description: Weaker version of rexlimiv 2421. (Contributed by FL, 19-Sep-2011.) |
Ref | Expression |
---|---|
rexlimivw.1 | ⊢ (φ → ψ) |
Ref | Expression |
---|---|
rexlimivw | ⊢ (∃x ∈ A φ → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexlimivw.1 | . . 3 ⊢ (φ → ψ) | |
2 | 1 | a1i 9 | . 2 ⊢ (x ∈ A → (φ → ψ)) |
3 | 2 | rexlimiv 2421 | 1 ⊢ (∃x ∈ A φ → ψ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ 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: r19.29vva 2450 eliun 3652 reusv3i 4157 elrnmptg 4529 fun11iun 5090 fmpt 5262 fliftfun 5379 elrnmpt2 5556 releldm2 5753 tfrlem4 5870 iinerm 6114 isfi 6177 ltbtwnnqq 6398 recexprlemlol 6598 recexprlemupu 6600 |
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