Theorem syl2im 34

Description: Replace two antecedents. Implication-only version of syl2an 463. (Contributed by Wolf Lammen, 14-May-2013.)

Hypotheses

Ref	Expression
syl2im.1	⊢ (φ → ψ)
syl2im.2	⊢ (χ → θ)
syl2im.3	⊢ (ψ → (θ → τ))

Assertion

Ref	Expression
syl2im	⊢ (φ → (χ → τ))

Proof of Theorem syl2im

Step	Hyp	Ref	Expression
1		syl2im.1	. 2 ⊢ (φ → ψ)
2		syl2im.2	. . 3 ⊢ (χ → θ)
3		syl2im.3	. . 3 ⊢ (ψ → (θ → τ))
4	2, 3	syl5 28	. 2 ⊢ (ψ → (χ → τ))
5	1, 4	syl 15	1 ⊢ (φ → (χ → τ))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  sylc  56  bi3ant  280  sp  1747  spOLD  1748  hbimdOLD  1816  dvelimv  1939  a16g  1945  ltfintr  4460