Theorem a1i13 24

Description: Add two antecedents to a wff. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1i13.1	⊢ (𝜓 → 𝜃)

Assertion

Ref	Expression
a1i13	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Proof of Theorem a1i13

Step	Hyp	Ref	Expression
1		a1i13.1	. . 3 ⊢ (𝜓 → 𝜃)
2	1	a1d 22	. 2 ⊢ (𝜓 → (𝜒 → 𝜃))
3	2	a1i 9	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  xpfi  7239  seq3fveq2  10927  seq3shft2  10933  seqshft2g  10934  seq3split  10940  seqsplitg  10941