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Mirrors > Home > HOLE Home > Th. List > ax4g | Unicode version |
Description: If ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ax4g.1 |
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ax4g.2 |
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Ref | Expression |
---|---|
ax4g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wal 134 |
. . . 4
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2 | ax4g.1 |
. . . 4
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3 | 1, 2 | wc 50 |
. . 3
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4 | 3 | trud 27 |
. 2
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5 | ax4g.2 |
. . . 4
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6 | 2, 5 | wc 50 |
. . 3
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7 | 4 | ax-cb1 29 |
. . . . . 6
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8 | 7 | id 25 |
. . . . 5
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9 | 2 | alval 142 |
. . . . . 6
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10 | 7, 9 | a1i 28 |
. . . . 5
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11 | 8, 10 | mpbi 82 |
. . . 4
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12 | 2, 5, 11 | ceq1 89 |
. . 3
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13 | 5, 4 | hbth 109 |
. . 3
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14 | 6, 12, 13 | eqtri 95 |
. 2
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15 | 4, 14 | mpbir 87 |
1
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Colors of variables: type var term |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-simpl 20 ax-simpr 21 ax-id 24 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-wctl 31 ax-wctr 32 ax-weq 40 ax-refl 42 ax-eqmp 45 ax-ded 46 ax-wct 47 ax-wc 49 ax-ceq 51 ax-wv 63 ax-wl 65 ax-beta 67 ax-distrc 68 ax-leq 69 ax-wov 71 ax-eqtypi 77 ax-eqtypri 80 ax-hbl1 103 ax-17 105 ax-inst 113 |
This theorem depends on definitions: df-ov 73 df-al 126 |
This theorem is referenced by: ax4 150 cla4v 152 |
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