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Mirrors > Home > ILE Home > Th. List > xchbinx | GIF version |
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.) |
Ref | Expression |
---|---|
xchbinx.1 | ⊢ (𝜑 ↔ ¬ 𝜓) |
xchbinx.2 | ⊢ (𝜓 ↔ 𝜒) |
Ref | Expression |
---|---|
xchbinx | ⊢ (𝜑 ↔ ¬ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xchbinx.1 | . 2 ⊢ (𝜑 ↔ ¬ 𝜓) | |
2 | xchbinx.2 | . . 3 ⊢ (𝜓 ↔ 𝜒) | |
3 | 2 | notbii 658 | . 2 ⊢ (¬ 𝜓 ↔ ¬ 𝜒) |
4 | 1, 3 | bitri 183 | 1 ⊢ (𝜑 ↔ ¬ 𝜒) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 |
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-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: xchbinxr 673 necon3abii 2363 elirr 4500 en2lp 4513 dm0rn0 4803 |
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