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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm13.196a | Structured version Visualization version Unicode version |
Description: Theorem *13.196 in [WhiteheadRussell] p. 179. The only difference is the position of the substituted variable. (Contributed by Andrew Salmon, 3-Jun-2011.) |
Ref | Expression |
---|---|
pm13.196a |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbelx 2287 |
. 2
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2 | sb56 2081 |
. 2
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3 | sbn 2220 |
. . . . 5
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4 | 3 | imbi2i 314 |
. . . 4
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5 | con2b 336 |
. . . 4
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6 | df-ne 2624 |
. . . . . 6
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7 | 6 | bicomi 206 |
. . . . 5
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8 | 7 | imbi2i 314 |
. . . 4
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9 | 4, 5, 8 | 3bitri 275 |
. . 3
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10 | 9 | albii 1691 |
. 2
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11 | 1, 2, 10 | 3bitri 275 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-ex 1664 df-nf 1668 df-sb 1798 df-ne 2624 |
This theorem is referenced by: (None) |
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