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Mirrors > Home > MPE Home > Th. List > ax12vALT | Structured version Visualization version Unicode version |
Description: Alternate proof of ax12v 1951, shorter, but depending on more axioms. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
ax12vALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 |
. . . 4
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2 | axc16 2043 |
. . . 4
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3 | 1, 2 | syl5 32 |
. . 3
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4 | 3 | a1d 25 |
. 2
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5 | axc15 2153 |
. 2
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6 | 4, 5 | pm2.61i 169 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-12 1950 ax-13 2104 |
This theorem depends on definitions: df-bi 190 df-an 378 df-ex 1672 df-nf 1676 |
This theorem is referenced by: (None) |
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