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Mirrors > Home > ILE Home > Th. List > imim21b | Unicode version |
Description: Simplify an implication between two implications when the antecedent of the first is a consequence of the antecedent of the second. The reverse form is useful in producing the successor step in induction proofs. (Contributed by Paul Chapman, 22-Jun-2011.) (Proof shortened by Wolf Lammen, 14-Sep-2013.) |
Ref | Expression |
---|---|
imim21b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi2.04 246 | . 2 | |
2 | pm5.5 240 | . . . . 5 | |
3 | 2 | imbi1d 229 | . . . 4 |
4 | 3 | imim2i 12 | . . 3 |
5 | 4 | pm5.74d 180 | . 2 |
6 | 1, 5 | syl5bb 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
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