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Mirrors > Home > NFE Home > Th. List > ax11vALT | Unicode version |
Description: Alternate proof of ax11v 2096 that avoids Theorem ax16 2045 and is proved directly from ax-11 1746 rather than via ax11o 1994. (Contributed by Jim Kingdon, 15-Dec-2017.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
ax11vALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1951 |
. 2
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2 | ax-17 1616 |
. . . . 5
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3 | ax-11 1746 |
. . . . 5
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4 | 2, 3 | syl5 28 |
. . . 4
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5 | equequ2 1686 |
. . . . 5
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6 | 5 | imbi1d 308 |
. . . . . . 7
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7 | 6 | albidv 1625 |
. . . . . 6
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8 | 7 | imbi2d 307 |
. . . . 5
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9 | 5, 8 | imbi12d 311 |
. . . 4
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10 | 4, 9 | mpbii 202 |
. . 3
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11 | 10 | exlimiv 1634 |
. 2
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12 | 1, 11 | ax-mp 5 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: (None) |
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