Theorem adantrrr 319

Description: Deduction adding a conjunct to an antecedent.

Hypothesis

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

Assertion

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

Proof of Theorem adantrrr

Step	Hyp	Ref	Expression
1		adantr2.1	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
2	1	a1d 14	. . 3 |- ((ph /\ (ps /\ ch)) -> (ta -> th))
3	2	exp32 294	. 2 |- (ph -> (ps -> (ch -> (ta -> th))))
4	3	imp45 290	1 |- ((ph /\ (ps /\ (ch /\ ta ))) -> th)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  zornlem6 3608

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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