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Mirrors > Home > ILE Home > Th. List > sb6 | Unicode version |
Description: Equivalence for substitution. Compare Theorem 6.2 of [Quine] p. 40. Also proved as Lemmas 16 and 17 of [Tarski] p. 70. (Contributed by NM, 18-Aug-1993.) (Revised by NM, 14-Apr-2008.) |
Ref | Expression |
---|---|
sb6 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb56 1897 |
. . 3
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2 | 1 | anbi2i 457 |
. 2
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3 | df-sb 1774 |
. 2
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4 | ax-4 1521 |
. . 3
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5 | 4 | pm4.71ri 392 |
. 2
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6 | 2, 3, 5 | 3bitr4i 212 |
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-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-sb 1774 |
This theorem is referenced by: sb5 1899 sbnv 1900 sbanv 1901 sbi1v 1903 sbi2v 1904 hbs1 1950 2sb6 1996 sbcom2v 1997 sb6a 2000 sb7af 2005 sbalyz 2011 sbal1yz 2013 exsb 2020 sbal2 2032 cbvabw 2312 nfabdw 2351 csbcow 3083 |
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