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Mirrors > Home > MPE Home > Th. List > nfimd | Structured version Visualization version Unicode version |
Description: If in a context is not free in and , it is not free in . Deduction form of nfimt 1821. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) df-nf 1710 changed. (Revised by Wolf Lammen, 18-Sep-2021.) |
Ref | Expression |
---|---|
nfimd.1 | |
nfimd.2 |
Ref | Expression |
---|---|
nfimd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfimd.1 | . 2 | |
2 | nfimd.2 | . 2 | |
3 | nfimt2 1822 | . 2 | |
4 | 1, 2, 3 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-nf 1710 |
This theorem is referenced by: nfand 1826 nfbid 1832 nfim1 2067 hbimd 2126 dvelimhw 2173 dvelimf 2334 nfmod2 2483 nfrald 2944 nfifd 4114 nfixp 7927 axrepndlem1 9414 axrepndlem2 9415 axunndlem1 9417 axunnd 9418 axpowndlem2 9420 axpowndlem3 9421 axpowndlem4 9422 axregndlem2 9425 axregnd 9426 axinfndlem1 9427 axinfnd 9428 axacndlem4 9432 axacndlem5 9433 axacnd 9434 bj-dvelimdv 32834 wl-mo2df 33352 wl-mo2t 33357 riotasv2d 34243 nfintd 42420 |
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