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Mirrors > Home > HOLE Home > Th. List > ax5 | Unicode version |
Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105. (Contributed by Mario Carneiro, 10-Oct-2014.) |
Ref | Expression |
---|---|
ax5.1 |
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ax5.2 |
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Ref | Expression |
---|---|
ax5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax5.2 |
. . . . . 6
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2 | ax5.1 |
. . . . . . . 8
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3 | 2 | ax4 150 |
. . . . . . 7
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4 | wal 134 |
. . . . . . . 8
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5 | wim 137 |
. . . . . . . . . 10
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6 | 5, 2, 1 | wov 72 |
. . . . . . . . 9
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7 | 6 | wl 66 |
. . . . . . . 8
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8 | 4, 7 | wc 50 |
. . . . . . 7
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9 | 3, 8 | adantl 56 |
. . . . . 6
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10 | 6 | ax4 150 |
. . . . . . 7
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11 | 3 | ax-cb1 29 |
. . . . . . 7
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12 | 10, 11 | adantr 55 |
. . . . . 6
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13 | 1, 9, 12 | mpd 156 |
. . . . 5
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14 | wv 64 |
. . . . . 6
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15 | 4, 14 | ax-17 105 |
. . . . . . 7
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16 | 6, 14 | ax-hbl1 103 |
. . . . . . 7
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17 | 4, 7, 14, 15, 16 | hbc 110 |
. . . . . 6
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18 | 2 | wl 66 |
. . . . . . 7
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19 | 2, 14 | ax-hbl1 103 |
. . . . . . 7
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20 | 4, 18, 14, 15, 19 | hbc 110 |
. . . . . 6
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21 | 8, 14, 11, 17, 20 | hbct 155 |
. . . . 5
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22 | 13, 21 | alrimi 182 |
. . . 4
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23 | 22 | ex 158 |
. . 3
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24 | wtru 43 |
. . 3
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25 | 23, 24 | adantl 56 |
. 2
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26 | 25 | ex 158 |
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-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-distrl 70 ax-wov 71 ax-eqtypi 77 ax-eqtypri 80 ax-hbl1 103 ax-17 105 ax-inst 113 ax-eta 177 |
This theorem depends on definitions: df-ov 73 df-al 126 df-an 128 df-im 129 |
This theorem is referenced by: ax11 214 |
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