Theorem adantlrl 314

Description: Deduction adding a conjunct to an antecedent.

Hypothesis

Ref	Expression
adantl2.1	|- (((ph /\ ps) /\ ch) -> th)

Assertion

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

Proof of Theorem adantlrl

Step	Hyp	Ref	Expression
1		adantl2.1	. . . 4 |- (((ph /\ ps) /\ ch) -> th)
2	1	exp31 293	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	a1d 14	. 2 |- (ph -> (ta -> (ps -> (ch -> th))))
4	3	imp42 287	1 |- (((ph /\ (ta /\ ps)) /\ ch) -> th)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  prlem936b 3948  qbtwnre 4650

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

metamath.org