Theorem anc2ri 303

Description: Deduction conjoining antecedent to right of consequent in nested implication.

Hypothesis

Ref	Expression
anc2ri.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
anc2ri	|- (ph -> (ps -> (ch /\ ph)))

Proof of Theorem anc2ri

Step	Hyp	Ref	Expression
1		anc2ri.1	. 2 |- (ph -> (ps -> ch))
2		anc2r 301	. 2 |- ((ph -> (ps -> ch)) -> (ph -> (ps -> (ch /\ ph))))
3	1, 2	ax-mp 7	1 |- (ph -> (ps -> (ch /\ ph)))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  fv3 3724  lmfexlem1 7907

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

Copyright terms: Public domain