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Mirrors > Home > HOLE Home > Th. List > ax14 | Unicode version |
Description: Axiom of Equality. Axiom scheme C12' in [Megill] p. 448 (p. 16 of the preprint). It is a special case of Axiom B8 (p. 75) of system S2 of [Tarski] p. 77. (Contributed by Mario Carneiro, 10-Oct-2014.) |
Ref | Expression |
---|---|
ax14.1 |
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ax14.2 |
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ax14.3 |
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Ref | Expression |
---|---|
ax14 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wtru 43 |
. . . . . 6
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2 | ax14.1 |
. . . . . . 7
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3 | ax14.2 |
. . . . . . 7
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4 | 2, 3 | weqi 76 |
. . . . . 6
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5 | 1, 4 | wct 48 |
. . . . 5
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6 | ax14.3 |
. . . . . 6
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7 | 2, 6 | wc 50 |
. . . . 5
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8 | 5, 7 | simpr 23 |
. . . 4
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9 | 1, 4 | simpr 23 |
. . . . . 6
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10 | 2, 6, 9 | ceq1 89 |
. . . . 5
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11 | 10, 7 | adantr 55 |
. . . 4
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12 | 8, 11 | mpbi 82 |
. . 3
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13 | 12 | ex 158 |
. 2
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14 | 13 | ex 158 |
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-distrl 70 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-an 128 df-im 129 |
This theorem is referenced by: (None) |
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