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Mirrors > Home > ILE Home > Th. List > simplbiim | Unicode version |
Description: Implication from an eliminated conjunct equivalent to the antecedent. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
simplbiim.1 | |
simplbiim.2 |
Ref | Expression |
---|---|
simplbiim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simplbiim.1 | . 2 | |
2 | simplbiim.2 | . . 3 | |
3 | 2 | adantl 271 | . 2 |
4 | 1, 3 | sylbi 119 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 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: zltaddlt1le 9028 oddnn02np1 10280 |
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