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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 40 | . . 3 |
4 | 3 | ibd 167 | . 2 |
5 | pm5.21ndd.2 | . . . . 5 | |
6 | 5, 2 | syld 40 | . . . 4 |
7 | bicom1 122 | . . . 4 | |
8 | 6, 7 | syl6 29 | . . 3 |
9 | 8 | ibd 167 | . 2 |
10 | 4, 9 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm5.21nd 825 sbcrext 2835 rmob 2850 epelg 4027 eqbrrdva 4505 relbrcnvg 4704 fmptco 5330 ovelrn 5649 brtpos2 5866 brdomg 6229 genpelvl 6610 genpelvu 6611 fzoval 9005 clim 9802 |
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