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Mirrors > Home > MPE Home > Th. List > nfpred | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for the predecessor class. (Contributed by Scott Fenton, 9-Jun-2018.) |
Ref | Expression |
---|---|
nfpred.1 | |
nfpred.2 | |
nfpred.3 |
Ref | Expression |
---|---|
nfpred |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pred 5680 | . 2 | |
2 | nfpred.2 | . . 3 | |
3 | nfpred.1 | . . . . 5 | |
4 | 3 | nfcnv 5301 | . . . 4 |
5 | nfpred.3 | . . . . 5 | |
6 | 5 | nfsn 4242 | . . . 4 |
7 | 4, 6 | nfima 5474 | . . 3 |
8 | 2, 7 | nfin 3820 | . 2 |
9 | 1, 8 | nfcxfr 2762 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wnfc 2751 cin 3573 csn 4177 ccnv 5113 cima 5117 cpred 5679 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 |
This theorem is referenced by: nfwrecs 7409 nfwsuc 31764 nfwlim 31768 |
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