Theorem adantl5r 522

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

Hypothesis

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

Assertion

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

Proof of Theorem adantl5r

Step	Hyp	Ref	Expression
1		adantl5r.1	. . . 4 |- ( ( ( ( ( ( ph /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) -> ka )
2	1	ex 114	. . 3 |- ( ( ( ( ( ph /\ ze ) /\ si ) /\ rh ) /\ mu ) -> ( la -> ka ) )
3	2	adantl4r 514	. 2 |- ( ( ( ( ( ( ph /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) -> ( la -> ka ) )
4	3	imp 123	1 |- ( ( ( ( ( ( ( ph /\ et ) /\ ze ) /\ si ) /\ rh ) /\ mu ) /\ la ) -> ka )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  adantl6r  523