Theorem axc4i 1957

Description: Inference version of axc4 1915. (Contributed by NM, 3-Jan-1993.)

Hypothesis

Ref	Expression
axc4i.1	|- ( A. x ph -> ps )

Assertion

Ref	Expression
axc4i	|- ( A. x ph -> A. x ps )

Proof of Theorem axc4i

Step	Hyp	Ref	Expression
1		nfa1 1956	. 2 |- F/ x A. x ph
2		axc4i.1	. 2 |- ( A. x ph -> ps )
3	1, 2	alrimi 1932	1 |- ( A. x ph -> A. x ps )

Syntax hints:   -> wi 4   A.wal 1435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-12 1909

This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662

This theorem is referenced by:  hbae  2115  hbsb2  2157  hbsb2a  2159  hbsb2e  2160  reu6  3195  axunndlem1  8964  axacndlem3  8978  axacndlem5  8980  axacnd  8981  bj-nfs1t  31211  bj-hbsb2v  31275  bj-hbsb2av  31277  bj-hbaeb2  31327  frege93  36459  pm11.57  36646  pm11.59  36648  axc5c4c711toc7  36662  axc11next  36664  hbalg  36829  ax6e2eq  36831  ax6e2eqVD  37214