Metamath Proof Explorer


Theorem ad11antr

Description: Deduction adding 11 conjuncts to antecedent. (Contributed by Thierry Arnoux, 27-Sep-2025)

Ref Expression
Hypothesis ad11antr.1
|- ( ph -> ps )
Assertion ad11antr
|- ( ( ( ( ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) /\ ka ) /\ nu ) -> ps )

Proof

Step Hyp Ref Expression
1 ad11antr.1
 |-  ( ph -> ps )
2 1 adantr
 |-  ( ( ph /\ ch ) -> ps )
3 2 ad10antr
 |-  ( ( ( ( ( ( ( ( ( ( ( ( ph /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) /\ ka ) /\ nu ) -> ps )