Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ancomsimp | GIF version |
Description: Closed form of ancoms 255. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
ancomsimp | ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 253 | . 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑)) | |
2 | 1 | imbi1i 227 | 1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: ralcomf 2471 |
Copyright terms: Public domain | W3C validator |