Theorem ax5d 1919

Description: Version of ax-5 1918 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders. (Contributed by NM, 1-Mar-2013.)

Assertion

Ref	Expression
ax5d	⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))

Distinct variable group:   𝜓,𝑥

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem ax5d

Step	Hyp	Ref	Expression
1		ax-5 1918	. 2 ⊢ (𝜓 → ∀𝑥𝜓)
2	1	a1i 11	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜓))

Syntax hints:   → wi 4  ∀wal 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-5 1918

This theorem is referenced by:  ax13w  2138