Theorem adantrll 402

Description: Deduction adding a conjunct to 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 379	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	a1d 12	. 2 |- (ph -> (ta -> (ps -> (ch -> th))))
4	3	imp44 371	1 |- ((ph /\ ((ta /\ ps) /\ ch)) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  distrlem4pr 5142  climsqueeze 7140  climsqueeze2 7141  caucvglem6 7162  blss 7850  lmcau 7993  bcthlem17 8012  lnopcon 9958  lnfncon 9985  mdslmd3 10254

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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