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Mirrors > Home > MPE Home > Th. List > equsex | Structured version Visualization version Unicode version |
Description: An equivalence related to implicit substitution. See equsexv 2065 for a version with a dv condition which does not require ax-13 2090. See equsexALT 2130 for an alternate proof. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Feb-2018.) |
Ref | Expression |
---|---|
equsex.nf |
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equsex.1 |
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Ref | Expression |
---|---|
equsex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsex.nf |
. . 3
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2 | equsex.1 |
. . . 4
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3 | 2 | biimpa 487 |
. . 3
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4 | 1, 3 | exlimi 1994 |
. 2
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5 | 1, 2 | equsal 2127 |
. . 3
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6 | equs4 2126 |
. . 3
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7 | 5, 6 | sylbir 217 |
. 2
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8 | 4, 7 | impbii 191 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-12 1932 ax-13 2090 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1663 df-nf 1667 |
This theorem is referenced by: equsexh 2131 sb5rf 2250 |
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