Theorem sps-o 39933

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 39908	. 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 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-c5 39908

This theorem is used by:  axc5c711toc7  39945  axc11n-16  39963  ax12eq  39966  ax12el  39967  ax12inda  39973  ax12v2-o  39974  axc11-o  39976