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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 | |
pm5.21nd.2 | |
pm5.21nd.3 |
Ref | Expression |
---|---|
pm5.21nd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.21nd.1 | . . 3 | |
2 | 1 | ex 114 | . 2 |
3 | pm5.21nd.2 | . . 3 | |
4 | 3 | ex 114 | . 2 |
5 | pm5.21nd.3 | . . 3 | |
6 | 5 | a1i 9 | . 2 |
7 | 2, 4, 6 | pm5.21ndd 694 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 |
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 4685 fvelimab 5470 releldm2 6076 relelec 6462 fzrev3 9860 elfzp12 9872 eltg 12210 eltg2 12211 cncnp2m 12389 |
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