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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 2908 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | 1 | nfsbc1 3823 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1781 [wsbc 3804 |
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 2110 ax-9 2118 ax-10 2141 ax-11 2158 ax-12 2178 ax-ext 2711 |
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 2718 df-cleq 2732 df-clel 2819 df-nfc 2895 df-sbc 3805 |
This theorem is referenced by: elrabsf 3853 cbvralcsf 3966 reusngf 4696 rexreusng 4703 reuprg0 4727 rmosn 4744 rabsnifsb 4747 euotd 5532 reuop 6324 frpoinsg 6375 wfisgOLD 6386 elfvmptrab1w 7056 elfvmptrab1 7057 ralrnmptw 7128 ralrnmpt 7130 oprabv 7510 elovmporab 7696 elovmporab1w 7697 elovmporab1 7698 ovmpt3rabdm 7709 elovmpt3rab1 7710 tfisg 7891 tfindes 7900 findes 7940 dfopab2 8093 dfoprab3s 8094 ralxpes 8177 ralxp3es 8180 frpoins3xpg 8181 frpoins3xp3g 8182 mpoxopoveq 8260 findcard2 9230 ac6sfi 9348 indexfi 9430 frinsg 9820 nn0ind-raph 12743 uzind4s 12973 fzrevral 13669 rabssnn0fi 14037 prmind2 16732 elmptrab 23856 isfildlem 23886 2sqreulem4 27516 gropd 29066 grstructd 29067 rspc2daf 32495 opreu2reuALT 32505 bnj919 34743 bnj1468 34822 bnj110 34834 bnj607 34892 bnj873 34900 bnj849 34901 bnj1388 35009 bnj1489 35032 setinds 35742 dfon2lem1 35747 rdgssun 37344 indexa 37693 indexdom 37694 sdclem2 37702 sdclem1 37703 fdc1 37706 alrimii 38079 riotasv2s 38914 sbccomieg 42749 rexrabdioph 42750 rexfrabdioph 42751 aomclem6 43016 pm14.24 44401 or2expropbilem2 46948 or2expropbi 46949 ich2exprop 47345 ichnreuop 47346 ichreuopeq 47347 prproropreud 47383 reupr 47396 reuopreuprim 47400 |
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