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  2323  eleq2w2  2732  eqeq1dALT  2739  eleq2dALT  2823  nfeqd  2909  funun  6544  fununi  6573  findcard  9098  findcard2  9099  ssfi  9107  ttrclselem2  9647  axpowndlem4  10523  axregndlem2  10526  axinfnd  10529  prcdnq  10916  dfrtrcl2  15024  relexpindlem  15025  bnj1379  34972  bnj1052  35117  bnj1118  35126  bnj1154  35141  bnj1280  35162  gblacfnacd  35284  onvf1odlem4  35288  mh-setind  36718  mh-setindnd  36719  dftrcl3  44147  dfrtrcl3  44160  vk15.4j  44955  hbimpg  44981  pgindnf  50191