Theorem 3adant3l 855

Description: Deduction adding a conjunct to antecedent.

Hypothesis

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

Assertion

Ref	Expression
3adant3l	|- ((ph /\ ps /\ (ta /\ ch)) -> th)

Proof of Theorem 3adant3l

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ((ph /\ ps /\ ch) -> th)
2	1	3com13 837	. . 3 |- ((ch /\ ps /\ ph) -> th)
3	2	3adant1l 851	. 2 |- (((ta /\ ch) /\ ps /\ ph) -> th)
4	3	3com13 837	1 |- ((ph /\ ps /\ (ta /\ ch)) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 774

This theorem is referenced by:  ecopoprtrn 4308  nvaddsub4 8266  adjlnopt 10010

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 776

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