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Theorem orim1d 711
Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)
Hypothesis
Ref Expression
orim1d.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
orim1d (𝜑 → ((𝜓𝜃) → (𝜒𝜃)))

Proof of Theorem orim1d
StepHypRef Expression
1 orim1d.1 . 2 (𝜑 → (𝜓𝜒))
2 idd 21 . 2 (𝜑 → (𝜃𝜃))
31, 2orim12d 710 1 (𝜑 → ((𝜓𝜃) → (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  pm2.38  727  pm2.73  730  pm2.74  731  pm2.8  734  pm2.82  736  unss1  3139  acexmidlemcase  5534  nn0ge2m1nn  8298
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