Theorem e21an 16599

Description: Conjunction form of e21 16598.

Hypotheses

Ref	Expression
e21an.1	|- . ph, ps   ⊢   ch .
e21an.2	|- . ph   ⊢   th .
e21an.3	|- ((ch /\ th) -> ta)

Assertion

Ref	Expression
e21an	|- . ph, ps   ⊢   ta .

Proof of Theorem e21an

Step	Hyp	Ref	Expression
1		e21an.1	. 2 |- . ph, ps   ⊢   ch .
2		e21an.2	. 2 |- . ph   ⊢   th .
3		e21an.3	. . 3 |- ((ch /\ th) -> ta)
4	3	ex 402	. 2 |- (ch -> (th -> ta))
5	1, 2, 4	e21 16598	1 |- . ph, ps   ⊢   ta .

Syntax hints:   -> wi 3   /\ wa 240   . vd1 16479   . vd2 16488

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 164  df-an 242  df-vd1 16480  df-vd2 16489

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