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Mirrors > Home > MPE Home > Th. List > dral1ALT | Structured version Visualization version Unicode version |
Description: Alternate proof of dral1 2161, shorter but requiring ax-11 1922. (Contributed by NM, 24-Nov-1994.) (Proof shortened by Wolf Lammen, 22-Apr-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
dral1.1 |
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Ref | Expression |
---|---|
dral1ALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dral1.1 |
. . 3
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2 | 1 | dral2 2160 |
. 2
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3 | axc11 2150 |
. . 3
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4 | axc112 2022 |
. . 3
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5 | 3, 4 | impbid 194 |
. 2
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6 | 2, 5 | bitrd 257 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1666 df-nf 1670 |
This theorem is referenced by: (None) |
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