Theorem 3ad2antr3 1195

Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 30-Dec-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	|- ( ( ph /\ ch ) -> th )

Assertion

Ref	Expression
3ad2antr3	|- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )

Proof of Theorem 3ad2antr3

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ( ( ph /\ ch ) -> th )
2	1	adantrl 482	. 2 |- ( ( ph /\ ( ta /\ ch ) ) -> th )
3	2	3adantr1 1187	1 |- ( ( ph /\ ( ps /\ ta /\ ch ) ) -> th )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  ordwe  4723  grprcan  13842  grpsubrcan  13886  grpaddsubass  13895  mhmmnd  13919