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Mirrors > Home > HOLE Home > Th. List > ax8 | Unicode version |
Description: Axiom of Equality. Axiom scheme C8' in [Megill] p. 448 (p. 16 of the preprint). Also appears as Axiom C7 of [Monk2] p. 105. |
Ref | Expression |
---|---|
ax8.1 |
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ax8.2 |
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ax8.3 |
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Ref | Expression |
---|---|
ax8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax8.2 |
. . . . 5
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2 | ax8.1 |
. . . . . 6
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3 | 2, 1 | weqi 68 |
. . . . . . 7
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4 | ax8.3 |
. . . . . . . 8
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5 | 2, 4 | weqi 68 |
. . . . . . 7
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6 | 3, 5 | simpl 22 |
. . . . . 6
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7 | 2, 6 | eqcomi 70 |
. . . . 5
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8 | 3, 5 | simpr 23 |
. . . . 5
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9 | 1, 7, 8 | eqtri 85 |
. . . 4
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10 | 9 | ex 148 |
. . 3
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11 | wtru 40 |
. . 3
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12 | 10, 11 | adantl 51 |
. 2
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13 | 12 | ex 148 |
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-refl 39 ax-eqmp 42 ax-ded 43 ax-ceq 46 ax-beta 60 ax-distrc 61 ax-leq 62 ax-distrl 63 ax-hbl1 93 ax-17 95 ax-inst 103 |
This theorem depends on definitions: df-ov 65 df-an 118 df-im 119 |
This theorem is referenced by: (None) |
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