Theorem r19.20sii 1699

Description: Inference quantifying antecedent, nested antecedent, and consequent, with a strong hypothesis.

Hypothesis

Ref	Expression
r19.20sii.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
r19.20sii	|- (A.x e. A ph -> (A.x e. A ps -> A.x e. A ch))

Proof of Theorem r19.20sii

Step	Hyp	Ref	Expression
1		r19.20sii.1	. . 3 |- (ph -> (ps -> ch))
2	1	r19.20si 1698	. 2 |- (A.x e. A ph -> A.x e. A (ps -> ch))
3		r19.20 1694	. 2 |- (A.x e. A (ps -> ch) -> (A.x e. A ps -> A.x e. A ch))
4	2, 3	syl 10	1 |- (A.x e. A ph -> (A.x e. A ps -> A.x e. A ch))

Syntax hints:   -> wi 3  A.wral 1637

This theorem is referenced by:  ss2ixp 4338  ivthlem3 7218  iscms2lem4 7926

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972

This theorem depends on definitions:  df-bi 147  df-an 225  df-ral 1641

Copyright terms: Public domain