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Theorem jca31 292
Description: Join three consequents. (Contributed by Jeff Hankins, 1-Aug-2009.)
Hypotheses
Ref Expression
jca31.1 (φψ)
jca31.2 (φχ)
jca31.3 (φθ)
Assertion
Ref Expression
jca31 (φ → ((ψ χ) θ))

Proof of Theorem jca31
StepHypRef Expression
1 jca31.1 . . 3 (φψ)
2 jca31.2 . . 3 (φχ)
31, 2jca 290 . 2 (φ → (ψ χ))
4 jca31.3 . 2 (φθ)
53, 4jca 290 1 (φ → ((ψ χ) θ))
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-ia3 101
This theorem is referenced by:  3jca  1083  syl21anc  1133  f1oiso2  5409  nnnq0lem1  6428  prmuloc  6545  prsrlem1  6630  apreap  7331  lemulge11  7573  elnnz  7991  leexp1a  8923
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