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Theorem pm3.48 698
Description: Theorem *3.48 of [WhiteheadRussell] p. 114. (Contributed by NM, 28-Jan-1997.) (Revised by NM, 1-Dec-2012.)
Assertion
Ref Expression
pm3.48 (((φψ) (χθ)) → ((φ χ) → (ψ θ)))

Proof of Theorem pm3.48
StepHypRef Expression
1 orc 632 . . 3 (ψ → (ψ θ))
21imim2i 12 . 2 ((φψ) → (φ → (ψ θ)))
3 olc 631 . . 3 (θ → (ψ θ))
43imim2i 12 . 2 ((χθ) → (χ → (ψ θ)))
52, 4jaao 638 1 (((φψ) (χθ)) → ((φ χ) → (ψ θ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  orim12d  699
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