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Theorem anim12ii 325
Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007.) (Proof shortened by Wolf Lammen, 19-Jul-2013.)
Hypotheses
Ref Expression
anim12ii.1 (φ → (ψχ))
anim12ii.2 (θ → (ψτ))
Assertion
Ref Expression
anim12ii ((φ θ) → (ψ → (χ τ)))

Proof of Theorem anim12ii
StepHypRef Expression
1 anim12ii.1 . . 3 (φ → (ψχ))
21adantr 261 . 2 ((φ θ) → (ψχ))
3 anim12ii.2 . . 3 (θ → (ψτ))
43adantl 262 . 2 ((φ θ) → (ψτ))
52, 4jcad 291 1 ((φ θ) → (ψ → (χ τ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
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 is referenced by:  euim  1965  elex22  2563  funcnvuni  4911  bj-findis  9363
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