Theorem adantl5r

Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018)

	Ref	Expression
Hypothesis	adantl5r.1	|- ( ( ( ( ( ( ph /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) -> ka )
Assertion	adantl5r	|- ( ( ( ( ( ( ( ph /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) -> ka )

Proof

Step	Hyp	Ref	Expression
1		adantl5r.1	|- ( ( ( ( ( ( ph /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) -> ka )
2	1	ex	|- ( ( ( ( ( ph /\ ze ) /\ si ) /\ rh ) /\ mu ) -> ( la -> ka ) )
3	2	adantl4r	|- ( ( ( ( ( ( ph /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) -> ( la -> ka ) )
4	3	imp	|- ( ( ( ( ( ( ( ph /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) -> ka )