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Mirrors > Home > MPE Home > Th. List > axc14 | Structured version Visualization version Unicode version |
Description: Axiom ax-c14 32463 is redundant if we assume ax-5 1758.
Remark 9.6 in
[Megill] p. 448 (p. 16 of the preprint),
regarding axiom scheme C14'.
Note that |
Ref | Expression |
---|---|
axc14 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbn1 1916 |
. . . . 5
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2 | dveel2 2200 |
. . . . 5
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3 | 1, 2 | hbim1 2001 |
. . . 4
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4 | elequ1 1894 |
. . . . 5
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5 | 4 | imbi2d 318 |
. . . 4
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6 | 3, 5 | dvelim 2171 |
. . 3
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7 | nfa1 1979 |
. . . . 5
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8 | 7 | nfn 1983 |
. . . 4
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9 | 8 | 19.21 1987 |
. . 3
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10 | 6, 9 | syl6ib 230 |
. 2
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11 | 10 | pm2.86d 102 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 |
This theorem is referenced by: (None) |
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