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Mirrors > Home > ILE Home > Th. List > equsal | Unicode version |
Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 5-Feb-2018.) |
Ref | Expression |
---|---|
equsal.1 |
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equsal.2 |
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Ref | Expression |
---|---|
equsal |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsal.1 |
. . 3
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2 | 1 | 19.23 1657 |
. 2
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3 | equsal.2 |
. . . 4
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4 | 3 | pm5.74i 179 |
. . 3
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5 | 4 | albii 1447 |
. 2
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6 | a9e 1675 |
. . 3
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7 | 6 | a1bi 242 |
. 2
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8 | 2, 5, 7 | 3bitr4i 211 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-nf 1438 |
This theorem is referenced by: intirr 4933 fun11 5198 |
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