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Mirrors > Home > ILE Home > Th. List > pm5.21nd | Unicode version |
Description: Eliminate an antecedent implied by each side of a biconditional. (Contributed by NM, 20-Nov-2005.) (Proof shortened by Wolf Lammen, 4-Nov-2013.) |
Ref | Expression |
---|---|
pm5.21nd.1 |
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pm5.21nd.2 |
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pm5.21nd.3 |
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Ref | Expression |
---|---|
pm5.21nd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.21nd.1 |
. . 3
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2 | 1 | ex 114 |
. 2
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3 | pm5.21nd.2 |
. . 3
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4 | 3 | ex 114 |
. 2
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5 | pm5.21nd.3 |
. . 3
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6 | 5 | a1i 9 |
. 2
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7 | 2, 4, 6 | pm5.21ndd 695 |
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 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ideqg 4698 fvelimab 5485 releldm2 6091 relelec 6477 fzrev3 9898 elfzp12 9910 eltg 12260 eltg2 12261 cncnp2m 12439 |
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