Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > ad5ant12 | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) |
Ref | Expression |
---|---|
ad5ant2.1 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
ad5ant12 | ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad5ant2.1 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) | |
2 | 1 | ad3antrrr 728 | 1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ 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: fpwwe2 10057 swrdccatin1 14079 lo1bdd2 14873 funcpropd 17162 curf2ndf 17489 metcnp3 23142 perpneq 26492 fmla1 32627 fnchoice 41277 hoidmvle 42873 isomuspgrlem1 43983 |
Copyright terms: Public domain | W3C validator |