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Theorem orim2d 777
 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 775 1 (𝜑 → ((𝜃𝜓) → (𝜃𝜒)))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∨ wo 697 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-io 698 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  orim2  778  orbi2d  779  pm2.82  801  stdcndcOLD  831  pm2.13dc  870  exmid1dc  4118  acexmidlemcase  5762  poxp  6122  fodjuomnilemdc  7009  indpi  7143  suplocexprlemloc  7522  nneoor  9146  uzp1  9352  maxabslemlub  10972  xrmaxiflemlub  11010  exmidunben  11928  bj-nn0suc  13151  sbthomlem  13209
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