Theorem p6eqd 4241

Description: Equality deduction for the P6 operation. (Contributed by SF, 12-Jan-2015.)

Hypothesis

Ref	Expression
p6eqd.1	⊢ (φ → A = B)

Assertion

Ref	Expression
p6eqd	⊢ (φ → P6 A = P6 B)

Proof of Theorem p6eqd

Step	Hyp	Ref	Expression
1		p6eqd.1	. 2 ⊢ (φ → A = B)
2		p6eq 4239	. 2 ⊢ (A = B → P6 A = P6 B)
3	1, 2	syl 15	1 ⊢ (φ → P6 A = P6 B)

Syntax hints:   → wi 4   = wceq 1642   P6 cp6 4179

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260  df-p6 4192

This theorem is referenced by: (None)