Theorem ee11an 16580

Description: e11an 16579 without virtual deductions. syl22anc 1101 is also e11an 16579 without virtual deductions, exept with a different order of hypotheses.

Hypotheses

Ref	Expression
ee11an.1	|- (ph -> ps)
ee11an.2	|- (ph -> ch)
ee11an.3	|- ((ps /\ ch) -> th)

Assertion

Ref	Expression
ee11an	|- (ph -> th)

Proof of Theorem ee11an

Step	Hyp	Ref	Expression
1		ee11an.1	. 2 |- (ph -> ps)
2		ee11an.2	. 2 |- (ph -> ch)
3		ee11an.3	. . 3 |- ((ps /\ ch) -> th)
4	3	ex 402	. 2 |- (ps -> (ch -> th))
5	1, 2, 4	ee11 1268	1 |- (ph -> th)

Syntax hints:   -> wi 3   /\ wa 240

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

Copyright terms: Public domain