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Mirrors > Home > MPE Home > Th. List > cbvex2 | Structured version Unicode version |
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 16-Jun-2019.) |
Ref | Expression |
---|---|
cbval2.1 |
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cbval2.2 |
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cbval2.3 |
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cbval2.4 |
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cbval2.5 |
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Ref | Expression |
---|---|
cbvex2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbval2.1 |
. . . . 5
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2 | 1 | nfn 1840 |
. . . 4
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3 | cbval2.2 |
. . . . 5
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4 | 3 | nfn 1840 |
. . . 4
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5 | cbval2.3 |
. . . . 5
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6 | 5 | nfn 1840 |
. . . 4
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7 | cbval2.4 |
. . . . 5
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8 | 7 | nfn 1840 |
. . . 4
![]() ![]() ![]() ![]() ![]() |
9 | cbval2.5 |
. . . . 5
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10 | 9 | notbid 294 |
. . . 4
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11 | 2, 4, 6, 8, 10 | cbval2 1987 |
. . 3
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12 | 11 | notbii 296 |
. 2
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13 | 2exnaln 1621 |
. 2
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14 | 2exnaln 1621 |
. 2
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15 | 12, 13, 14 | 3bitr4i 277 |
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-11 1782 ax-12 1794 ax-13 1955 |
This theorem depends on definitions: df-bi 185 df-an 371 df-ex 1588 df-nf 1591 |
This theorem is referenced by: cbvex2v 1991 2eu6OLD 2381 cbvopab 4471 cbvoprab12 6272 |
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