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Mirrors > Home > MPE Home > Th. List > sbcom4 | Structured version Unicode version |
Description: Commutativity law for substitution. This theorem was incorrectly used as our previous version of pm11.07 2163 but may still be useful. (Contributed by Andrew Salmon, 17-Jun-2011.) (Proof shortened by Jim Kingdon, 22-Jan-2018.) |
Ref | Expression |
---|---|
sbcom4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1674 |
. . . . 5
![]() ![]() ![]() ![]() | |
2 | 1 | sbf 2081 |
. . . 4
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3 | 2 | sbbii 1709 |
. . 3
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4 | nfv 1674 |
. . . 4
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5 | 4 | sbf 2081 |
. . 3
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6 | 3, 5 | bitri 249 |
. 2
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7 | 1 | sbf 2081 |
. . . 4
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8 | 7 | sbbii 1709 |
. . 3
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9 | 4 | sbf 2081 |
. . 3
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10 | 8, 9 | bitri 249 |
. 2
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11 | 6, 10 | bitr4i 252 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-12 1794 ax-13 1955 |
This theorem depends on definitions: df-bi 185 df-an 371 df-ex 1588 df-nf 1591 df-sb 1703 |
This theorem is referenced by: (None) |
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