Theorem 3adantr3 806

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 436	. . 3 |- (((ps /\ ch) /\ ph) -> th)
3	2	3adantl3 803	. 2 |- (((ps /\ ch /\ ta) /\ ph) -> th)
4	3	ancoms 436	1 |- ((ph /\ (ps /\ ch /\ ta)) -> th)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 773

This theorem is referenced by:  3ad2antr1 810  3ad2antr2 811  3adant3r3 842  dfwe2 2925  tgioolem 7853  lmle 7895  grpnpncan 8029  nvsubadd 8215  dmdsl3t 10150

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 775

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