Theorem sps-o 40058

Description: Generalization of antecedent. (Contributed by NM, 5-Jan-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
sps-o.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
sps-o	⊢ (∀𝑥𝜑 → 𝜓)

Proof of Theorem sps-o

Step	Hyp	Ref	Expression
1		ax-c5 40033	. 2 ⊢ (∀𝑥𝜑 → 𝜑)
2		sps-o.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	syl 18	1 ⊢ (∀𝑥𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-c5 40033

This theorem is used by:  axc5c711toc7  40070  axc11n-16  40088  ax12eq  40091  ax12el  40092  ax12inda  40098  ax12v2-o  40099  axc11-o  40101