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Mirrors > Home > HOLE Home > Th. List > alval | Unicode version |
Description: Value of the for all predicate. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
alval.1 |
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Ref | Expression |
---|---|
alval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wal 134 |
. . 3
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2 | alval.1 |
. . 3
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3 | 1, 2 | wc 50 |
. 2
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4 | df-al 126 |
. . 3
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5 | 1, 2, 4 | ceq1 89 |
. 2
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6 | wv 64 |
. . . 4
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7 | wtru 43 |
. . . . 5
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8 | 7 | wl 66 |
. . . 4
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9 | 6, 8 | weqi 76 |
. . 3
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10 | weq 41 |
. . . 4
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11 | 6, 2 | weqi 76 |
. . . . 5
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12 | 11 | id 25 |
. . . 4
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13 | 10, 6, 8, 12 | oveq1 99 |
. . 3
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14 | 9, 2, 13 | cl 116 |
. 2
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15 | 3, 5, 14 | eqtri 95 |
1
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Colors of variables: type var term |
Syntax hints: tv 1
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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-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: ax4g 149 alrimiv 151 olc 164 orc 165 alrimi 182 |
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