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Mirrors > Home > MPE Home > Th. List > nffvmpt1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for mapping, special case. (Contributed by Mario Carneiro, 25-Dec-2016.) |
Ref | Expression |
---|---|
nffvmpt1 | ⊢ Ⅎ𝑥((𝑥 ∈ 𝐴 ↦ 𝐵)‘𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfmpt1 5218 | . 2 ⊢ Ⅎ𝑥(𝑥 ∈ 𝐴 ↦ 𝐵) | |
2 | nfcv 2908 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | 1, 2 | nffv 6857 | 1 ⊢ Ⅎ𝑥((𝑥 ∈ 𝐴 ↦ 𝐵)‘𝐶) |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2888 ↦ cmpt 5193 ‘cfv 6501 |
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 2708 |
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 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ral 3066 df-rex 3075 df-rab 3411 df-v 3450 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-br 5111 df-opab 5173 df-mpt 5194 df-iota 6453 df-fv 6509 |
This theorem is referenced by: fvmptt 6973 fmptco 7080 offval2f 7637 offval2 7642 ofrfval2 7643 mptelixpg 8880 dom2lem 8939 cantnflem1 9632 acni2 9989 axcc2 10380 seqof2 13973 rlim2 15385 ello1mpt 15410 o1compt 15476 sumfc 15601 fsum 15612 fsumf1o 15615 sumss 15616 fsumcvg2 15619 fsumadd 15632 isummulc2 15654 fsummulc2 15676 fsumrelem 15699 isumshft 15731 zprod 15827 fprod 15831 prodfc 15835 fprodf1o 15836 fprodmul 15850 fproddiv 15851 iserodd 16714 prdsbas3 17370 prdsdsval2 17373 invfuc 17870 yonedalem4b 18172 gsumdixp 20040 evlslem4 21500 elptr2 22941 ptunimpt 22962 ptcldmpt 22981 ptclsg 22982 txcnp 22987 ptcnplem 22988 cnmpt1t 23032 cnmptk2 23053 flfcnp2 23374 voliun 24934 mbfeqalem1 25021 mbfpos 25031 mbfposb 25033 mbfsup 25044 mbfinf 25045 mbflim 25048 i1fposd 25088 isibl2 25147 itgmpt 25163 itgeqa 25194 itggt0 25224 itgcn 25225 limcmpt 25263 lhop2 25395 itgsubstlem 25428 itgsubst 25429 elplyd 25579 coeeq2 25619 dgrle 25620 ulmss 25772 itgulm2 25784 leibpi 26308 rlimcnp 26331 o1cxp 26340 lgamgulmlem2 26395 lgamgulmlem6 26399 fmptcof2 31615 itggt0cn 36177 elrfirn2 41048 eq0rabdioph 41128 monotoddzz 41296 aomclem8 41417 fmuldfeq 43898 vonioo 44997 |
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