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Theorem pm5.21nii 607
Description: Eliminate an antecedent implied by each side of a biconditional. (Contributed by NM, 21-May-1999.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypotheses
Ref Expression
pm5.21ni.1 (φψ)
pm5.21ni.2 (χψ)
pm5.21nii.3 (ψ → (φχ))
Assertion
Ref Expression
pm5.21nii (φχ)

Proof of Theorem pm5.21nii
StepHypRef Expression
1 pm5.21ni.1 . . . 4 (φψ)
2 pm5.21nii.3 . . . 4 (ψ → (φχ))
31, 2syl 14 . . 3 (φ → (φχ))
43ibi 165 . 2 (φχ)
5 pm5.21ni.2 . . . 4 (χψ)
65, 2syl 14 . . 3 (χ → (φχ))
76ibir 166 . 2 (χφ)
84, 7impbii 117 1 (φχ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  anxordi  1274  elrabf  2671  sbcco  2760  sbc5  2762  sbcan  2780  sbcor  2782  sbcal  2785  sbcex2  2787  eldif  2902  elun  3059  elin  3101  eluni  3555  eliun  3633  elopab  3967  opelopabsb  3969  opeliunxp  4320  opeliunxp2  4401  elxp4  4733  elxp5  4734  fsn2  5260  isocnv2  5375  elxp6  5717  elxp7  5718  brtpos2  5786  tpostpos  5799  ecdmn0m  6057  elinp  6326  recexprlemell  6454  recexprlemelu  6455  gt0srpr  6493  ltresr  6548
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