Theorem anc2l 300

Description: Conjoin antecedent to left of consequent in nested implication.

Assertion

Ref	Expression
anc2l	|- ((ph -> (ps -> ch)) -> (ph -> (ps -> (ph /\ ch))))

Proof of Theorem anc2l

Step	Hyp	Ref	Expression
1		pm3.2 283	. . 3 |- (ph -> (ch -> (ph /\ ch)))
2	1	imim2d 25	. 2 |- (ph -> ((ps -> ch) -> (ps -> (ph /\ ch))))
3	2	a2i 9	1 |- ((ph -> (ps -> ch)) -> (ph -> (ps -> (ph /\ ch))))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  anc2li 302  imdistan 442  suppsr2 5203

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

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