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Mirrors > Home > ILE Home > Th. List > cdeqim | Unicode version |
Description: Distribute conditional equality over implication. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
cdeqnot.1 | CondEq |
cdeqim.1 | CondEq |
Ref | Expression |
---|---|
cdeqim | CondEq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdeqnot.1 | . . . 4 CondEq | |
2 | 1 | cdeqri 2801 | . . 3 |
3 | cdeqim.1 | . . . 4 CondEq | |
4 | 3 | cdeqri 2801 | . . 3 |
5 | 2, 4 | imbi12d 232 | . 2 |
6 | 5 | cdeqi 2800 | 1 CondEq |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 CondEqwcdeq 2798 |
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 df-cdeq 2799 |
This theorem is referenced by: (None) |
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