Theorem 19.21bi 2197

Description: Inference form of 19.21 2215 and also deduction form of sp 2191. (Contributed by NM, 26-May-1993.)

Hypothesis

Ref	Expression
19.21bi.1	⊢ (𝜑 → ∀𝑥𝜓)

Assertion

Ref	Expression
19.21bi	⊢ (𝜑 → 𝜓)

Proof of Theorem 19.21bi

Step	Hyp	Ref	Expression
1		19.21bi.1	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
2		sp 2191	. 2 ⊢ (∀𝑥𝜓 → 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-12 2185

This theorem depends on definitions:  df-bi 207  df-ex 1782

This theorem is referenced by:  19.21bbi  2198  axc7e  2324  eleq2w2  2733  eqeq1dALT  2740  eleq2dALT  2824  nfeqd  2910  funun  6546  fununi  6575  findcard  9100  findcard2  9101  ssfi  9109  ttrclselem2  9647  axpowndlem4  10523  axregndlem2  10526  axinfnd  10529  prcdnq  10916  dfrtrcl2  14997  relexpindlem  14998  bnj1379  35006  bnj1052  35151  bnj1118  35160  bnj1154  35175  bnj1280  35196  gblacfnacd  35318  onvf1odlem4  35322  mh-setind  36688  mh-setindnd  36689  dftrcl3  44076  dfrtrcl3  44089  vk15.4j  44884  hbimpg  44910  pgindnf  50075