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Mirrors > Home > ILE Home > Th. List > equsalh | Unicode version |
Description: A useful equivalence related to substitution. New proofs should use equsal 1688 instead. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
equsalh.1 |
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equsalh.2 |
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Ref | Expression |
---|---|
equsalh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsalh.2 |
. . . . 5
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2 | equsalh.1 |
. . . . . 6
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3 | 2 | 19.3h 1515 |
. . . . 5
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4 | 1, 3 | syl6bbr 197 |
. . . 4
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5 | 4 | pm5.74i 179 |
. . 3
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6 | 5 | albii 1429 |
. 2
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7 | 2 | a1d 22 |
. . . 4
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8 | 2, 7 | alrimih 1428 |
. . 3
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9 | ax9o 1659 |
. . 3
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10 | 8, 9 | impbii 125 |
. 2
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11 | 6, 10 | bitr4i 186 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-4 1470 ax-i9 1493 ax-ial 1497 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: sb6x 1735 dvelimfALT2 1771 dvelimALT 1961 dvelimfv 1962 dvelimor 1969 |
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