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Mirrors > Home > ILE Home > Th. List > con2biidc | GIF version |
Description: A contraposition inference. (Contributed by Jim Kingdon, 15-Mar-2018.) |
Ref | Expression |
---|---|
con2biidc.1 | ⊢ (DECID 𝜓 → (𝜑 ↔ ¬ 𝜓)) |
Ref | Expression |
---|---|
con2biidc | ⊢ (DECID 𝜓 → (𝜓 ↔ ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2biidc.1 | . . . 4 ⊢ (DECID 𝜓 → (𝜑 ↔ ¬ 𝜓)) | |
2 | 1 | bicomd 141 | . . 3 ⊢ (DECID 𝜓 → (¬ 𝜓 ↔ 𝜑)) |
3 | 2 | con1biidc 877 | . 2 ⊢ (DECID 𝜓 → (¬ 𝜑 ↔ 𝜓)) |
4 | 3 | bicomd 141 | 1 ⊢ (DECID 𝜓 → (𝜓 ↔ ¬ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 105 DECID wdc 834 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 |
This theorem depends on definitions: df-bi 117 df-dc 835 |
This theorem is referenced by: dfexdc 1501 nnedc 2352 |
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