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Mirrors > Home > MPE Home > Th. List > ancomst | Structured version Visualization version GIF version |
Description: Closed form of ancoms 461. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
ancomst | ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 463 | . 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑)) | |
2 | 1 | imbi1i 352 | 1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 ∧ wa 398 |
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 209 df-an 399 |
This theorem is referenced by: sbcom2 2167 ralcom 3357 ralcomf 3360 ovolgelb 24084 itg2leub 24338 nmoubi 28552 wl-sbcom2d 34801 ifpidg 39863 undmrnresiss 39970 ntrneiiso 40447 expcomdg 40840 |
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