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Theorem simp3r 932
Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)
Assertion
Ref Expression
simp3r ((φ ψ (χ θ)) → θ)

Proof of Theorem simp3r
StepHypRef Expression
1 simpr 103 . 2 ((χ θ) → θ)
213ad2ant3 926 1 ((φ ψ (χ θ)) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 884
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  df-3an 886
This theorem is referenced by:  simpl3r  959  simpr3r  965  simp13r  1019  simp23r  1025  simp33r  1031  issod  4047  tfisi  4253  fvun1  5182  f1oiso2  5409  tfrlem5  5871  ecopovtrn  6139  ecopovtrng  6142  addassnqg  6366  ltsonq  6382  ltanqg  6384  ltmnqg  6385  addassnq0  6444  mulasssrg  6666  distrsrg  6667  lttrsr  6670  ltsosr  6672  ltasrg  6678  mulextsr1lem  6686  mulextsr1  6687  axmulass  6737  axdistr  6738  reapmul1  7359  mulcanap  7408  mulcanap2  7409  divassap  7431  divdirap  7436  div11ap  7439  apmul1  7526  ltdiv1  7595  ltmuldiv  7601  ledivmul  7604  lemuldiv  7608  lediv2  7618  ltdiv23  7619  lediv23  7620  expaddzap  8933  expmulzap  8935
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