Theorem 3adantr3 820

Description: Deduction adding a conjunct to antecedent.

Hypothesis

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

Assertion

Ref	Expression
3adantr3	|- ((ph /\ (ps /\ ch /\ ta)) -> th)

Proof of Theorem 3adantr3

Step	Hyp	Ref	Expression
1		3adantr.1	. . . 4 |- ((ph /\ (ps /\ ch)) -> th)
2	1	ancoms 447	. . 3 |- (((ps /\ ch) /\ ph) -> th)
3	2	3adantl3 817	. 2 |- (((ps /\ ch /\ ta) /\ ph) -> th)
4	3	ancoms 447	1 |- ((ph /\ (ps /\ ch /\ ta)) -> th)

Syntax hints:   -> wi 3   /\ wa 230   /\ w3a 787

This theorem is referenced by:  3ad2antr1 824  3ad2antr2 825  3adant3r3 856  dfwe2 2992  tgioolem 7999  lmle 8045  grpnpncan 8178  nvsubadd 8359  dmdsl3 10326

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 154  df-an 232  df-3an 789

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