Theorem e03an 16610

Description: Conjunction form of e03 16608.

Hypotheses

Ref	Expression
e03an.1	|- ph
e03an.2	|- . ps, ch, th   ⊢   ta .
e03an.3	|- ((ph /\ ta) -> et)

Assertion

Ref	Expression
e03an	|- . ps, ch, th   ⊢   et .

Proof of Theorem e03an

Step	Hyp	Ref	Expression
1		e03an.1	. 2 |- ph
2		e03an.2	. 2 |- . ps, ch, th   ⊢   ta .
3		e03an.3	. . 3 |- ((ph /\ ta) -> et)
4	3	ex 402	. 2 |- (ph -> (ta -> et))
5	1, 2, 4	e03 16608	1 |- . ps, ch, th   ⊢   et .

Syntax hints:   -> wi 3   /\ wa 240   . vd3 16493

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-3an 860  df-vd3 16494

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