Theorem 3ad2antr1 811

Description: Deduction adding a conjuncts to antecedent.

Hypothesis

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

Assertion

Ref	Expression
3ad2antr1	|- ((ph /\ (ch /\ ps /\ ta)) -> th)

Proof of Theorem 3ad2antr1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 |- ((ph /\ ch) -> th)
2	1	adantrr 395	. 2 |- ((ph /\ (ch /\ ps)) -> th)
3	2	3adantr3 807	1 |- ((ph /\ (ch /\ ps /\ ta)) -> th)

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

This theorem is referenced by:  dfwe2 2932  dnsconst 7767  metcni2 7878  tgioolem 7897  lmbr 7911  lmle 7943  nvcni 8315  nvcni2 8316  nvcni3 8317  ismonb2 10689

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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