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Mirrors > Home > MPE Home > Th. List > ancomst | Structured version Visualization version GIF version |
Description: Closed form of ancoms 451. (Contributed by Alan Sare, 31-Dec-2011.) |
Ref | Expression |
---|---|
ancomst | ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 453 | . 2 ⊢ ((𝜑 ∧ 𝜓) ↔ (𝜓 ∧ 𝜑)) | |
2 | 1 | imbi1i 341 | 1 ⊢ (((𝜑 ∧ 𝜓) → 𝜒) ↔ ((𝜓 ∧ 𝜑) → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 ∧ wa 385 |
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 199 df-an 386 |
This theorem is referenced by: sbcom2 2561 sbcom2OLD 2562 ralcomf 3275 ovolgelb 23585 itg2leub 23839 nmoubi 28144 wl-sbcom2d 33826 ifpidg 38608 undmrnresiss 38681 ntrneiiso 39159 expcomdg 39474 |
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