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Mirrors > Home > ILE Home > Th. List > reximdv | GIF version |
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998.) |
Ref | Expression |
---|---|
reximdv.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
reximdv | ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → ∃𝑥 ∈ 𝐴 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reximdv.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | a1d 22 | . 2 ⊢ (𝜑 → (𝑥 ∈ 𝐴 → (𝜓 → 𝜒))) |
3 | 2 | reximdvai 2564 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → ∃𝑥 ∈ 𝐴 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2135 ∃wrex 2443 |
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 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-ral 2447 df-rex 2448 |
This theorem is referenced by: r19.12 2570 reusv3 4432 rexxfrd 4435 iunpw 4452 fvelima 5532 carden2bex 7136 prnmaddl 7422 prarloclem5 7432 prarloc2 7436 genprndl 7453 genprndu 7454 ltpopr 7527 recexprlemm 7556 recexprlemopl 7557 recexprlemopu 7559 recexprlem1ssl 7565 recexprlem1ssu 7566 cauappcvgprlemupu 7581 caucvgprlemupu 7604 caucvgprprlemupu 7632 caucvgsrlemoffres 7732 map2psrprg 7737 resqrexlemgt0 10948 subcn2 11238 bezoutlembz 11922 pythagtriplem19 12191 tgcl 12605 neiss 12691 ssnei2 12698 tgcnp 12750 cnptopco 12763 cnptopresti 12779 lmtopcnp 12791 blssexps 12970 blssex 12971 mopni3 13025 neibl 13032 metss 13035 metcnp3 13052 rescncf 13109 limcresi 13176 |
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