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Theorem orim2d 789
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)
Hypothesis
Ref Expression
orim1d.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
orim2d (𝜑 → ((𝜃𝜓) → (𝜃𝜒)))

Proof of Theorem orim2d
StepHypRef Expression
1 idd 21 . 2 (𝜑 → (𝜃𝜃))
2 orim1d.1 . 2 (𝜑 → (𝜓𝜒))
31, 2orim12d 787 1 (𝜑 → ((𝜃𝜓) → (𝜃𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 709
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  orim2  790  orbi2d  791  pm2.82  813  stdcndcOLD  847  pm2.13dc  886  exmid1dc  4218  acexmidlemcase  5891  poxp  6257  fodjuomnilemdc  7172  omniwomnimkv  7195  exmidontriimlem1  7250  indpi  7371  suplocexprlemloc  7750  nneoor  9385  uzp1  9591  maxabslemlub  11248  xrmaxiflemlub  11288  exmidunben  12477  bj-nn0suc  15174  sbthomlem  15232
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