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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-stand | Unicode version |
Description: The conjunction of two stable formulas is stable. Deduction form of bj-stan 14381. Its proof is shorter (when counting all steps, including syntactic steps), so one could prove it first and then bj-stan 14381 from it, the usual way. (Contributed by BJ, 24-Nov-2023.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-stand.1 |
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bj-stand.2 |
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Ref | Expression |
---|---|
bj-stand |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-nnan 14370 |
. . 3
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2 | bj-stand.1 |
. . . . 5
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3 | df-stab 831 |
. . . . 5
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4 | 2, 3 | sylib 122 |
. . . 4
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5 | bj-stand.2 |
. . . . 5
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6 | df-stab 831 |
. . . . 5
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7 | 5, 6 | sylib 122 |
. . . 4
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8 | 4, 7 | anim12d 335 |
. . 3
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9 | 1, 8 | syl5 32 |
. 2
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10 | df-stab 831 |
. 2
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11 | 9, 10 | sylibr 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 |
This theorem depends on definitions: df-bi 117 df-stab 831 |
This theorem is referenced by: (None) |
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