Theorem adantrrl 402

Description: Deduction adding a conjunct to antecedent.

Hypothesis

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

Assertion

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

Proof of Theorem adantrrl

Step	Hyp	Ref	Expression
1		adantr2.1	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
2	1	exp32 377	. . 3 |- (ph -> (ps -> (ch -> th)))
3	2	a1dd 42	. 2 |- (ph -> (ps -> (ta -> (ch -> th))))
4	3	imp45 372	1 |- ((ph /\ (ps /\ (ta /\ ch))) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  zorn2lem6 4793  ltmul12it 5841  climsqueeze 7140  climsqueeze2 7141  neissex 7738  iscau3 7938  iscau4 7940  grprcan 8063  mdslmd3 10259

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

Copyright terms: Public domain