Theorem 3adant1l 854

Description: Deduction adding a conjunct to antecedent.

Hypothesis

Ref	Expression
3adant1l.1	|- ((ph /\ ps /\ ch) -> th)

Assertion

Ref	Expression
3adant1l	|- (((ta /\ ph) /\ ps /\ ch) -> th)

Proof of Theorem 3adant1l

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3expb 836	. . 3 |- ((ph /\ (ps /\ ch)) -> th)
3	2	adantll 394	. 2 |- (((ta /\ ph) /\ (ps /\ ch)) -> th)
4	3	3impb 831	1 |- (((ta /\ ph) /\ ps /\ ch) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 777

This theorem is referenced by:  3adant2l 856  3adant3l 858  lt2mul2divt 5874  climcmplem 7137  mulc1cncf 7279  spwpr4OLD 8658  spwpr4aOLD 8659

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  df-3an 779

Copyright terms: Public domain