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Mirrors > Home > ILE Home > Th. List > sbcom | Unicode version |
Description: A commutativity law for substitution. (Contributed by NM, 27-May-1997.) (Proof rewritten by Jim Kingdon, 22-Mar-2018.) |
Ref | Expression |
---|---|
sbcom |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbco3 1986 |
. 2
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2 | sbcocom 1982 |
. 2
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3 | sbcocom 1982 |
. 2
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4 | 1, 2, 3 | 3bitr3i 210 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: sb9 1991 |
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