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Mirrors > Home > MPE Home > Th. List > nfnfcALT | Structured version Visualization version Unicode version |
Description: Alternate proof of nfnfc 2774. Shorter but requiring more axioms. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfnfc.1 |
Ref | Expression |
---|---|
nfnfcALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nfc 2753 | . 2 | |
2 | nfnfc.1 | . . . . 5 | |
3 | 2 | nfcri 2758 | . . . 4 |
4 | 3 | nfnf 2158 | . . 3 |
5 | 4 | nfal 2153 | . 2 |
6 | 1, 5 | nfxfr 1779 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wal 1481 wnf 1708 wcel 1990 wnfc 2751 |
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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-cleq 2615 df-clel 2618 df-nfc 2753 |
This theorem is referenced by: (None) |
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