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Mirrors > Home > MPE Home > Th. List > xchnxbi | Structured version Visualization version GIF version |
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.) |
Ref | Expression |
---|---|
xchnxbi.1 | ⊢ (¬ 𝜑 ↔ 𝜓) |
xchnxbi.2 | ⊢ (𝜑 ↔ 𝜒) |
Ref | Expression |
---|---|
xchnxbi | ⊢ (¬ 𝜒 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xchnxbi.2 | . . 3 ⊢ (𝜑 ↔ 𝜒) | |
2 | 1 | notbii 309 | . 2 ⊢ (¬ 𝜑 ↔ ¬ 𝜒) |
3 | xchnxbi.1 | . 2 ⊢ (¬ 𝜑 ↔ 𝜓) | |
4 | 2, 3 | bitr3i 265 | 1 ⊢ (¬ 𝜒 ↔ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 195 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 |
This theorem is referenced by: xchnxbir 322 ioran 510 pm5.24 934 2mo 2539 necon1bbii 2831 nabbi 2884 psslinpr 9732 isprm2lem 15232 |
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