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Mirrors > Home > ILE Home > Th. List > pm5.21ndd | Unicode version |
Description: Eliminate an antecedent implied by each side of a biconditional, deduction version. (Contributed by Paul Chapman, 21-Nov-2012.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
pm5.21ndd.1 | |
pm5.21ndd.2 | |
pm5.21ndd.3 |
Ref | Expression |
---|---|
pm5.21ndd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.21ndd.1 | . . . 4 | |
2 | pm5.21ndd.3 | . . . 4 | |
3 | 1, 2 | syld 45 | . . 3 |
4 | 3 | ibd 177 | . 2 |
5 | pm5.21ndd.2 | . . . . 5 | |
6 | 5, 2 | syld 45 | . . . 4 |
7 | bicom1 130 | . . . 4 | |
8 | 6, 7 | syl6 33 | . . 3 |
9 | 8 | ibd 177 | . 2 |
10 | 4, 9 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: pm5.21nd 901 sbcrext 2981 rmob 2996 epelg 4207 eqbrrdva 4704 relbrcnvg 4913 fmptco 5579 ovelrn 5912 brtpos2 6141 elpmg 6551 brdomg 6635 elfi2 6853 genpelvl 7313 genpelvu 7314 fzoval 9918 clim 11043 cnrest2 12394 cnptoprest2 12398 lmss 12404 reopnap 12696 limcdifap 12789 |
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