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Mirrors > Home > MPE Home > Th. List > nfsbc1v | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfsbc1v | ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2904 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | nfsbc1 3817 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1781 [wsbc 3798 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2105 ax-9 2113 ax-10 2136 ax-11 2153 ax-12 2173 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1540 df-ex 1778 df-nf 1782 df-sb 2065 df-clab 2712 df-cleq 2726 df-clel 2813 df-nfc 2890 df-sbc 3799 |
This theorem is referenced by: elrabsf 3847 cbvralcsf 3960 reusngf 4696 rexreusng 4703 reuprg0 4727 rmosn 4744 rabsnifsb 4747 euotd 5536 reuop 6323 frpoinsg 6374 wfisgOLD 6385 elfvmptrab1w 7054 elfvmptrab1 7055 ralrnmptw 7126 ralrnmpt 7128 oprabv 7506 elovmporab 7692 elovmporab1w 7693 elovmporab1 7694 ovmpt3rabdm 7705 elovmpt3rab1 7706 tfisg 7887 tfindes 7896 findes 7936 dfopab2 8089 dfoprab3s 8090 ralxpes 8173 ralxp3es 8176 frpoins3xpg 8177 frpoins3xp3g 8178 mpoxopoveq 8256 findcard2 9226 ac6sfi 9344 indexfi 9426 frinsg 9816 nn0ind-raph 12739 uzind4s 12969 fzrevral 13665 rabssnn0fi 14033 prmind2 16726 elmptrab 23849 isfildlem 23879 2sqreulem4 27507 gropd 29057 grstructd 29058 rspc2daf 32486 opreu2reuALT 32496 bnj919 34735 bnj1468 34814 bnj110 34826 bnj607 34884 bnj873 34892 bnj849 34893 bnj1388 35001 bnj1489 35024 setinds 35734 dfon2lem1 35739 rdgssun 37292 indexa 37641 indexdom 37642 sdclem2 37650 sdclem1 37651 fdc1 37654 alrimii 38027 riotasv2s 38862 sbccomieg 42686 rexrabdioph 42687 rexfrabdioph 42688 aomclem6 42956 pm14.24 44341 or2expropbilem2 46882 or2expropbi 46883 ich2exprop 47277 ichnreuop 47278 ichreuopeq 47279 prproropreud 47315 reupr 47328 reuopreuprim 47332 |
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