Theorem ral2imi 2169

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

Hypothesis

Ref	Expression
ral2imi.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
ral2imi	|- (A.x e. A ph -> (A.x e. A ps -> A.x e. A ch))

Proof of Theorem ral2imi

Step	Hyp	Ref	Expression
1		ral2imi.1	. . 3 |- (ph -> (ps -> ch))
2	1	ralimi 2168	. 2 |- (A.x e. A ph -> A.x e. A (ps -> ch))
3		ralim 2164	. 2 |- (A.x e. A (ps -> ch) -> (A.x e. A ps -> A.x e. A ch))
4	2, 3	syl 12	1 |- (A.x e. A ph -> (A.x e. A ps -> A.x e. A ch))

Syntax hints:   -> wi 3  A.wral 2105

This theorem is referenced by:  rexim 2194  r19.26 2219  ss2ixp 5413  ivthlem3 8545  iscms2lem4 9270  unprj 14511  inttop2 14863  intcont 14914

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ral 2109

Copyright terms: Public domain