Theorem 3adantll2 39202

Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Hypothesis

Ref	Expression
3adantll2.1	|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
3adantll2	|- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> ta )

Proof of Theorem 3adantll2

Step	Hyp	Ref	Expression
1		simpll1 1100	. . 3 |- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> ph )
2		simpll3 1102	. . 3 |- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> ps )
3	1, 2	jca 554	. 2 |- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> ( ph /\ ps ) )
4		simplr 792	. 2 |- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> ch )
5		simpr 477	. 2 |- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> th )
6		3adantll2.1	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
7	3, 4, 5, 6	syl21anc 1325	1 |- ( ( ( ( ph /\ et /\ ps ) /\ ch ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  icccncfext  40100  fourierdlem42  40366