Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > pm4.76 | Structured version Visualization version GIF version |
Description: Theorem *4.76 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm4.76 | ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) ↔ (𝜑 → (𝜓 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jcab 907 | . 2 ⊢ ((𝜑 → (𝜓 ∧ 𝜒)) ↔ ((𝜑 → 𝜓) ∧ (𝜑 → 𝜒))) | |
2 | 1 | bicomi 214 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) ↔ (𝜑 → (𝜓 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ∧ wa 384 |
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 197 df-an 386 |
This theorem is referenced by: fun11 5963 axgroth4 9654 dford4 37596 undmrnresiss 37910 |
Copyright terms: Public domain | W3C validator |