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Theorem stoic4b 1319
Description: Stoic logic Thema 4 version b.

This is version b, which is with the phrase "or both". See stoic4a 1318 for more information. (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
Ref Expression
stoic4b.1 ((φ ψ) → χ)
stoic4b.2 (((χ φ ψ) θ) → τ)
Assertion
Ref Expression
stoic4b ((φ ψ θ) → τ)

Proof of Theorem stoic4b
StepHypRef Expression
1 stoic4b.1 . . 3 ((φ ψ) → χ)
213adant3 923 . 2 ((φ ψ θ) → χ)
3 simp1 903 . 2 ((φ ψ θ) → φ)
4 simp2 904 . 2 ((φ ψ θ) → ψ)
5 simp3 905 . 2 ((φ ψ θ) → θ)
6 stoic4b.2 . 2 (((χ φ ψ) θ) → τ)
72, 3, 4, 5, 6syl31anc 1137 1 ((φ ψ θ) → τ)
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: (None)
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