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Theorem ralrimivw 2483
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014.)
Hypothesis
Ref Expression
ralrimivw.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
ralrimivw  |-  ( ph  ->  A. x  e.  A  ps )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    A( x)

Proof of Theorem ralrimivw
StepHypRef Expression
1 ralrimivw.1 . . 3  |-  ( ph  ->  ps )
21a1d 22 . 2  |-  ( ph  ->  ( x  e.  A  ->  ps ) )
32ralrimiv 2481 1  |-  ( ph  ->  A. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1465   A.wral 2393
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-4 1472  ax-17 1491
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-ral 2398
This theorem is referenced by:  r19.27v  2536  r19.28v  2537  exse  4228  sosng  4582  dmxpm  4729  exse2  4883  funco  5133  acexmidlemph  5735  mpoeq12  5799  xpexgALT  5999  mpoexg  6077  rdgtfr  6239  rdgruledefgg  6240  rdgivallem  6246  frecabex  6263  frectfr  6265  omfnex  6313  oeiv  6320  uniqs  6455  sbthlemi5  6817  sbthlemi6  6818  updjud  6935  exmidfodomrlemim  7025  exmidaclem  7032  genpdisj  7299  ltexprlemloc  7383  recexprlemloc  7407  cauappcvgprlemrnd  7426  cauappcvgprlemdisj  7427  caucvgprlemrnd  7449  caucvgprlemdisj  7450  caucvgprprlemrnd  7477  caucvgprprlemdisj  7478  suplocexpr  7501  recan  10849  climconst  11027  sumeq2ad  11106  dvdsext  11480  neif  12237  lmconst  12312  cndis  12337
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