Theorem adantrll 316

Description: Deduction adding a conjunct to an antecedent.

Hypothesis

Ref	Expression
adantr2.1	|- ((ph /\ (ps /\ ch)) -> th)

Assertion

Ref	Expression
adantrll	|- ((ph /\ ((ta /\ ps) /\ ch)) -> th)

Proof of Theorem adantrll

Step	Hyp	Ref	Expression
1		adantr2.1	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
2	1	exp32 294	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	a1d 14	. 2 |- (ph -> (ta -> (ps -> (ch -> th))))
4	3	imp44 289	1 |- ((ph /\ ((ta /\ ps) /\ ch)) -> th)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  distrlem4pr 3924

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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