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Theorem syl2im 34
Description: Replace two antecedents. Implication-only version of syl2an 273. (Contributed by Wolf Lammen, 14-May-2013.)
Hypotheses
Ref Expression
syl2im.1 (φψ)
syl2im.2 (χθ)
syl2im.3 (ψ → (θτ))
Assertion
Ref Expression
syl2im (φ → (χτ))

Proof of Theorem syl2im
StepHypRef Expression
1 syl2im.1 . 2 (φψ)
2 syl2im.2 . . 3 (χθ)
3 syl2im.3 . . 3 (ψ → (θτ))
42, 3syl5 28 . 2 (ψ → (χτ))
51, 4syl 14 1 (φ → (χτ))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  sylc  56  bi3ant  213  pm3.12dc  864  pm3.13dc  865  nfrimi  1415  vtoclr  4331  funopg  4877  xpiderm  6113  ixxssixx  8541  difelfzle  8762  bj-inf2vnlem1  9430
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