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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 2590 | 1 ⊢ (𝜑 → (∃𝑥 ∈ 𝐴 𝜓 → ∃𝑥 ∈ 𝐴 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∈ wcel 2160 ∃wrex 2469 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-ral 2473 df-rex 2474 |
This theorem is referenced by: r19.12 2596 reusv3 4478 rexxfrd 4481 iunpw 4498 fvelima 5588 carden2bex 7219 prnmaddl 7520 prarloclem5 7530 prarloc2 7534 genprndl 7551 genprndu 7552 ltpopr 7625 recexprlemm 7654 recexprlemopl 7655 recexprlemopu 7657 recexprlem1ssl 7663 recexprlem1ssu 7664 cauappcvgprlemupu 7679 caucvgprlemupu 7702 caucvgprprlemupu 7730 caucvgsrlemoffres 7830 map2psrprg 7835 resqrexlemgt0 11064 subcn2 11354 bezoutlembz 12040 pythagtriplem19 12317 tgcl 14041 neiss 14127 ssnei2 14134 tgcnp 14186 cnptopco 14199 cnptopresti 14215 lmtopcnp 14227 blssexps 14406 blssex 14407 mopni3 14461 neibl 14468 metss 14471 metcnp3 14488 rescncf 14545 limcresi 14612 |
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