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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 1612 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 1442 |
. . . . 5
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4 | 1, 3 | syl6bbr 187 |
. . . 4
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5 | 4 | pm5.74i 169 |
. . 3
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6 | 5 | albii 1356 |
. 2
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7 | 2 | a1d 22 |
. . . 4
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8 | 2, 7 | alrimih 1355 |
. . 3
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9 | ax9o 1585 |
. . 3
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10 | 8, 9 | impbii 117 |
. 2
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11 | 6, 10 | bitr4i 176 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-i9 1420 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: sb6x 1659 dvelimfALT2 1695 dvelimALT 1883 dvelimfv 1884 dvelimor 1891 |
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