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Mirrors > Home > MPE Home > Th. List > nfima | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for image. (Contributed by NM, 30-Dec-1996.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
nfima.1 | ⊢ Ⅎ𝑥𝐴 |
nfima.2 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfima | ⊢ Ⅎ𝑥(𝐴 “ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ima 5650 | . 2 ⊢ (𝐴 “ 𝐵) = ran (𝐴 ↾ 𝐵) | |
2 | nfima.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | nfima.2 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
4 | 2, 3 | nfres 5943 | . . 3 ⊢ Ⅎ𝑥(𝐴 ↾ 𝐵) |
5 | 4 | nfrn 5911 | . 2 ⊢ Ⅎ𝑥ran (𝐴 ↾ 𝐵) |
6 | 1, 5 | nfcxfr 2902 | 1 ⊢ Ⅎ𝑥(𝐴 “ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2884 ran crn 5638 ↾ cres 5639 “ cima 5640 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-br 5110 df-opab 5172 df-xp 5643 df-cnv 5645 df-dm 5647 df-rn 5648 df-res 5649 df-ima 5650 |
This theorem is referenced by: nfimad 6026 csbima12 6035 nfpred 6262 nfsup 9395 nfoi 9458 nfseq 13925 gsum2d2 19759 ptbasfi 22955 mbfposr 25039 itg1climres 25102 limciun 25281 funimass4f 31604 poimirlem16 36144 poimirlem19 36147 aomclem8 41435 areaquad 41597 nfcoll 42628 binomcxplemdvbinom 42725 binomcxplemdvsum 42727 binomcxplemnotnn0 42728 rfcnpre1 43316 rfcnpre2 43328 smfpimcc 45139 |
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