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Mirrors > Home > ILE Home > Th. List > cdeqeq | Unicode version |
Description: Distribute conditional equality over equality. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
cdeqeq.1 | CondEq |
cdeqeq.2 | CondEq |
Ref | Expression |
---|---|
cdeqeq | CondEq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdeqeq.1 | . . . 4 CondEq | |
2 | 1 | cdeqri 2923 | . . 3 |
3 | cdeqeq.2 | . . . 4 CondEq | |
4 | 3 | cdeqri 2923 | . . 3 |
5 | 2, 4 | eqeq12d 2172 | . 2 |
6 | 5 | cdeqi 2922 | 1 CondEq |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1335 CondEqwcdeq 2920 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-cdeq 2921 |
This theorem is referenced by: (None) |
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